A sphere-equivalency approach for calculating the elastic property of an isotropic solid containing aligned inclusions: Modeling and experiment data verification

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. C239-C249
Author(s):  
Song Xu ◽  
Xiaoming Tang ◽  
Yuanda Su
Keyword(s):  
Elastic Properties ◽  
Elastic Wave Scattering ◽  
Fluid Saturation ◽  
Isotropic Solid ◽  
Improved Stability ◽  
High Crack ◽  
The Stability ◽  
Stability And Accuracy ◽  
Shallow Crust ◽  
Mean Square Errors

Accurate modeling of elastic properties of cracked rocks in the earth’s shallow crust has long been an important topic in the field of geophysics. A sphere-equivalency approach of elastic wave scattering was used to model the elastic moduli of an isotropic solid containing aligned cracks. The results were compared with those of the existing Eshelby-Cheng and Hudson’s theories for dry and fluid saturation conditions, showing remarkably improved stability and accuracy for high crack concentrations, especially for Hudson’s second-order model. The stability and accuracy of the new approach were determined for varying solid and crack parameters. Finally, the new and existing theories were applied to model the laboratory ultrasonic experimental data measured on artificially cracked samples with varying wave frequencies and crack concentrations. Compared to Hudson’s theory, the new model agrees significantly better with the data. Specifically, the root-mean-square errors of theoretical fitting to data from our model are generally smaller than those from the other two models. We have thus developed an effective tool for modeling elastic properties of cracked rocks.

scholarly journals A Class of Explicit Integrators with o-grid Interpolation for Solving Non-linear Systems of First Order ODEs

2020 ◽  
pp. 106-118
Author(s):  
U. W. Sirisena ◽  
S. I. Luka ◽  
S. Y. Yakubu
Keyword(s):  
Research Work ◽  
Stability And Convergence ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Improved Stability ◽  
Linear Problems ◽  
The Stability ◽  
Stability And Accuracy ◽  
Grid Interpolation

This research work is aimed at constructing a class of explicit integrators with improved stability and accuracy by incorporating an off-gird interpolation point for the purpose of making them effcient for solving stiff initial value problems. Accordingly, continuous formulations of a class of hybrid explicit integrators are derived using multi-step collocation method through matrix inversion technique, for step numbers k = 2; 3; 4: The discrete schemes were deduced from their respective continuous formulations. The stability and convergence analysis were carried out and shown to be A(α)-stable and convergent respectively. The discrete schemes when implemented as block integrators to solve some non-linear problems, it was observed that the results obtained compete favorably with the MATLAB ode23 solver.

scholarly journals Global Calibration Method of a Camera Using the Constraint of Line Features and 3D World Points

2016 ◽  
Vol 16 (4) ◽  
pp. 190-196 ◽  
Author(s):  
Guan Xu ◽  
Xinyuan Zhang ◽  
Xiaotao Li ◽  
Jian Su ◽  
Zhaobing Hao
Keyword(s):  
Calibration Method ◽  
Original Method ◽  
Transformation Matrix ◽  
Mean Values ◽  
Global Calibration ◽  
The Stability ◽  
Stability And Accuracy ◽  
Value Decomposition ◽  
Projective Lines ◽  
Mean Square Errors

Abstract We present a reliable calibration method using the constraint of 2D projective lines and 3D world points to elaborate the accuracy of the camera calibration. Based on the relationship between the 3D points and the projective plane, the constraint equations of the transformation matrix are generated from the 3D points and 2D projective lines. The transformation matrix is solved by the singular value decomposition. The proposed method is compared with the point-based calibration to verify the measurement validity. The mean values of the root-mean-square errors using the proposed method are 7.69×10−4, 6.98×10−4, 2.29×10−4, and 1.09×10−3 while the ones of the original method are 8.10×10−4, 1.29×10−2, 2.58×10−2, and 8.12×10−3. Moreover, the average logarithmic errors of the calibration method are evaluated and compared with the former method in different Gaussian noises and projective lines. The variances of the average errors using the proposed method are 1.70×10−5, 1.39×10−4, 1.13×10−4, and 4.06×10−4, which indicates the stability and accuracy of the method.

scholarly journals Underground Microseismic Event Monitoring and Localization within Sensor Networks

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2830
Author(s):  
Sili Wang ◽  
Mark P. Panning ◽  
Steven D. Vance ◽  
Wenzhan Song
Keyword(s):  
Sensor Networks ◽  
Real Time ◽  
Information Needs ◽  
Localization Algorithm ◽  
Distributed Sensors ◽  
Distributed Sensor ◽  
Microseismic Events ◽  
The Stability ◽  
Stability And Accuracy

Locating underground microseismic events is important for monitoring subsurface activity and understanding the planetary subsurface evolution. Due to bandwidth limitations, especially in applications involving planetarily-distributed sensor networks, networks should be designed to perform the localization algorithm in-situ, so that only the source location information needs to be sent out, not the raw data. In this paper, we propose a decentralized Gaussian beam time-reverse imaging (GB-TRI) algorithm that can be incorporated to the distributed sensors to detect and locate underground microseismic events with reduced usage of computational resources and communication bandwidth of the network. After the in-situ distributed computation, the final real-time location result is generated and delivered. We used a real-time simulation platform to test the performance of the system. We also evaluated the stability and accuracy of our proposed GB-TRI localization algorithm using extensive experiments and tests.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

scholarly journals A Digital Framework to Predict the Sunshine Requirements of Landscape Plants

2021 ◽  
Vol 11 (5) ◽  
pp. 2098
Author(s):  
Heyi Wei ◽  
Wenhua Jiang ◽  
Xuejun Liu ◽  
Bo Huang
Keyword(s):  
Solar Radiation ◽  
Plant Species ◽  
Large Scale ◽  
Normal Growth ◽  
Adaptive Selection ◽  
Landscape Plant ◽  
Landscape Plants ◽  
The Stability ◽  
Stability And Accuracy ◽  
The City

Knowledge of the sunshine requirements of landscape plants is important information for the adaptive selection and configuration of plants for urban greening, and is also a basic attribute of plant databases. In the existing studies, the light compensation point (LCP) and light saturation point (LSP) have been commonly used to indicate the shade tolerance for a specific plant; however, these values are difficult to adopt in practice because the landscape architect does not always know what range of solar radiation is the best for maintaining plant health, i.e., normal growth and reproduction. In this paper, to bridge the gap, we present a novel digital framework to predict the sunshine requirements of landscape plants. First, the research introduces the proposed framework, which is composed of a black-box model, solar radiation simulation, and a health standard system for plants. Then, the data fitting between solar radiation and plant growth response is used to obtain the value of solar radiation at different health levels. Finally, we adopt the LI-6400XT Portable Photosynthetic System (Li-Cor Inc., Lincoln, NE, USA) to verify the stability and accuracy of the digital framework through 15 landscape plant species of a residential area in the city of Wuhan, China, and also compared and analyzed the results of other researchers on the same plant species. The results show that the digital framework can robustly obtain the values of the healthy, sub-healthy, and unhealthy levels for the 15 landscape plant species. The purpose of this study is to provide an efficient forecasting tool for large-scale surveys of plant sunshine requirements. The proposed framework will be beneficial for the adaptive selection and configuration of urban plants and will facilitate the construction of landscape plant databases in future studies.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Modelling of the Power Interface of the Digital-Physical Hybrid Simulation System of a VSC-HVDC Based on Virtual Resistance Compensation

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 333
Author(s):  
Jian Le ◽  
Hao Zhang ◽  
Cao Wang ◽  
Xingrui Li ◽  
Jiangfeng Zhu
Keyword(s):  
Current Source ◽  
Hybrid Simulation ◽  
Simulation System ◽  
System Stability ◽  
Interface Model ◽  
Simulation Accuracy ◽  
Hvdc System ◽  
High Voltage Direct Current ◽  
The Stability ◽  
Stability And Accuracy

To enhance the stability and accuracy of the digital-physical hybrid simulation system of a modular multilevel converter-based high voltage direct current (MMC-HVDC) system, this paper presents an improved power interface modeling algorithm based on ideal transformer method (ITM). By analyzing the stability condition of a hybrid simulation system based on the ITM model, the current of a so-called virtual resistance is added to the control signal of the controlled current source in the digital subsystem, and the stability of the hybrid simulation system with the improved power interface model is analyzed. The value of the virtual resistance is optimized by comprehensively considering system stability and simulation precision. A two-terminal bipolar MMC-HVDC simulation system based on the proposed power interface model is established. The comparisons of the simulation results verify that the proposed method can effectively improve the stability of the hybrid simulation system, and at the same time has the advantages of high simulation accuracy and easy implementation.

scholarly journals Stabilizing immature breathing patterns of preterm infants using stochastic mechanosensory stimulation

2009 ◽  
Vol 107 (4) ◽  
pp. 1017-1027 ◽  
Author(s):  
Elisabeth Bloch-Salisbury ◽  
Premananda Indic ◽  
Frank Bednarek ◽  
David Paydarfar
Keyword(s):  
Preterm Infants ◽  
Respiratory Control ◽  
Behavioral State ◽  
Mean Square ◽  
Breathing Patterns ◽  
Nonlinear Properties ◽  
Improved Stability ◽  
Postconceptional Age ◽  
The Stability ◽  
Large Improvement

Breathing patterns in preterm infants consist of highly variable interbreath intervals (IBIs) that might originate from nonlinear properties of the respiratory oscillator and its input-output responses to peripheral and central signals. Here, we explore a property of nonlinear control, the potential for large improvement in the stability of breathing using low-level exogenous stochastic stimulation. Stimulation was administered to 10 preterm infants (postconceptional age: mean 33.3 wk, SD 1.7) using a mattress with embedded actuators that delivered small stochastic displacements (0.021 mm root mean square, 0.090 mm maximum, 30–60 Hz); this stimulus was subthreshold for causing arousal from sleep to wakefulness or other detectable changes in the behavioral state evaluated with polysomnography. We used a test-retest protocol with multiple 10-min intervals of stimulation, each paired with 10-min intervals of no stimulation. Stimulation induced an ∼50% reduction ( P = 0.003) in the variance of IBIs and an ∼50% reduction ( P = 0.002) in the incidence of IBIs > 5 s. The improved stability of eupneic breathing was associated with an ∼65% reduction ( P = 0.04) in the duration of O2 desaturation. Our findings suggest that nonlinear properties of the immature respiratory control system can be harnessed using afferent stimuli to stabilize eupneic breathing, thereby potentially reducing the incidence of apnea and hypoxia.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

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