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least squares method Prediction-based Spray and Focus Routing Protocol in Opportunistic Networks

2012 Asia Pacific Conference on Environmental Science and Technology(APEST 2012)

作者： Andy A.B. Rosli Saad Geophysics Section School of PhysicsUniversiti Sains Malaysia11800 USMPenangMalaysia

Soil is a heterogeneous medium which consist of liquid,solid and gases phases.The solid and liquid phases play an essential role in soil spontaneous electrical phenomena and in behaviour of electrical fields,artificially created in soil.A method is worked out to determine the soil friction coefficient and specific adhesion for clayey sand soil.The specific effective cohesion,specific internal friction angle and specific resistivity of tropical clayey sand soils were determined in this research.In order to determine the specific friction coefficient and specific adhesion of clayey sand soils,the soil slipping resistance should be assessed at several different values of pressure between the slipping surfaces.The direct shear test,resistivity test,soil’s consistency and atterberg limit tests were carried out in purposed to determine the physical characterizations of clayey sand soils.Base on the basic of this opinion,by the means of least squares method（LSM）,the soil’s friction coefficient and specific adhesion together with specific effective cohesion,specific internal friction angle and their specific resistivity of tropical clayey sand soils is successfully determined.This research also systematically investigates the physical behaviour and their correlations of clayey sand soils properties during fixed period which potentially for hazard assessment.

关键词： Friction coefficient Specific cohesion Resistivity least squares method Clayey sand.

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Least Squares Method Prediction-based Spray and Focus Routin...

Forecasting of Target Air Route Based on Weighted least squares method

2012 National Conference on Information Technology and Computer Science

作者： Zhuowei Shen Key Lab of Computer Network and Information Integration (Southeast University),MOE School of Computer Science and Engineering Southeast University Nanjing,China Ying Tu Key Lab of Computer Network and Information Integration (Southeast University),MOE School of Computer Science and Engineering Southeast University Nanjing,China

Opportunistic Networks develops rapidly in recent years.With the popularity of GPS （Global Positioning System）,velocity or position prediction plays an important role in opportunistic network routing.In this paper,a new opportunistic routing protocol named LSMPSF （least squares method Prediction-based Spray and Focus） is proposed.With least squares method,LSMPSF predicts velocity by curve fitting.According to the predicted velocities,it estimates the neighbor nodes’ delivery ratio and makes routing decision.Simulation results reveal that LSMPSF effectively increases the prediction accuracy and reduces resource consumption.Compared with SF and PROPHET,LSMPSF achieves better performance on delivery ratio and overhead ratio.

关键词： Opportunistic Networks Spray and Focus least squares method

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Forecasting of Target Air Route Based on Weighted Least Squa...

least square method based on Haar wavelet to solve multi-dimensional stochastic Ito-Volterra integral equations

第二十九届中国控制会议

作者： CAO Jian-Zhong,HUANG Jin-Qiu,CHEN Zhi-Ming Electronic Science Department,Huizhou University,Guangdong 516007,P.R.China

The azimuth and elevation variation rules of a short-range,low-flying target is firstly analyzed in this paper,then the target air route is predicted using a weighted least squares parabolic regression parameter estimation method-firstly the input signal is filtered,then one step prediction is carried out.This method has advantages of easier formula derivation and less intermediate variables.Simulation results show that by selection of forgetting factor of the historical data,the prediction of the target air route can be faster,stabler and more accurate.

关键词： Target Air Route least squares method Attenuation Factor Prediction

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Applied Mathematics(A Journal of Chinese Universities) 2023年第4期38卷 591-603页

作者： JIANG Guo KE Ting DENG Meng-ting School of Mathematics and Statistics Hubei Normal UniversityHuangshi 435002China

This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.

关键词： least squares method Haar wavelet Ito-Volterra integral equations integration operational matrix.

Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: Effects of different bases

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Science China Mathematics 2023年第1期66卷 191-220页

作者： Xiaolong Zhang John P.Boyd MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China Department of Climate&Space Sciences and Engineering University of MichiganAnn ArborMI 48109USA

When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary conditions.For homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients cn.If u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a constant.We prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the endpoints.Despite having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in x.Meanwhile,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference basis.Furthermore,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares method.We also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite truncation.But the premise is under the same basis,and when involving different bases,it may not be established yet.

关键词： Chebyshev polynomial interpolation endpoint singularities least squares method

A Reconstructed Discontinuous Approximation to Monge-Ampère Equation in least Square Formulation

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Advances in Applied Mathematics and Mechanics 2023年第5期15卷 1109-1141页

作者： Ruo Li Fanyi Yang CAPT LMAM and School of Mathematical SciencesPeking UniversityBeijing 100871China School of Mathematics Sichuan UniversityChengduSichuan 610064China

We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.

关键词： Monge-Ampère equation least squares method reconstructed discontinuous approximation

BENDING PROBLEM OF A FINITE COMPOSITE LAMINATED PLATE WEAKENED BY MULTIPLE ELLIPTICAL HOLES

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Acta Mechanica Solida Sinica 2013年第4期26卷 419-426页

作者： Chunjian Mao Xiwu Xu State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics

Based on the classical composite laminate theory,the bending problem of a finite composite plate weakened by multiple elliptical holes is studied by means of the complex variable method.The present work is intended to express the complex potentials in the form of Faber series aided by the use of the least squares boundary collocation techniques on the finite boundaries.As a result,concise and high accuracy solutions are presented for the stress distribution around the holes.Finally,numerical examples are presented to discuss the effects of some parameters on the stress concentration around the holes.

关键词： anisotropic plate bending finite plate elliptical holes Faber series least squares method

Prediction meta-models for the responses of a circular tunnel during earthquakes

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Underground Space 2019年第1期4卷 31-47页

作者： Nazim Abdul Nariman Raja Rizwan Hussain Mohammed A Msekh Peyman Karampour Engineering Department Sulaimaniya Health General DirectorateMinistry of HealthKurdistan RegionIraq Civil Engineering Department College of EngineeringKing Saud University11421 RiyadhSaudi Arabia Civil Engineering Department College of EngineeringUniversity of BabylonBabylonIraq Department of Mechanical Engineering Faculty of EngineeringArak UniversityArakIran

Three uncertain parameters(peak ground acceleration,soil density,and soil modulus of elasticity)have been studied with regard to their effects on the stability and damage of a circular tunnel during an earthquake.A time history of an actual earthquake in the literature with modification has been adopted in the numerical simulation and analysis of the tunnel responses.Meta-models have been constructed based on an experimental method with quadratic and interaction terms using matlab codes in order to predict the compressive damage,tensile damage,and the overall displacement of the tunnel.The results of the meta-models predicted a highly reasonable response of the tunnel with regard to the maximum principal stresses in the tunnel lining and predicted a remarkable response of the tunnel with respect to the overall displacement of the tunnel.Moreover,the peak ground acceleration was observed to exert the highest effect on the overall displacement of the tunnel,compared to the soil density and soil modulus of elasticity.Furthermore,the metamodels revealed the inverse relationship between the soil modulus of elasticity and the compressive and tensile damages of the tunnel lining.The meta-models exhibited high efficiency of representation of the behavior of the structural system during earthquakes.

关键词： Peak ground acceleration Ovalization Meta-model least squares method Compressive damage Tensile damage

Multi-channel signal parameters joint optimization for GNSS terminals

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Journal of Systems Engineering and Electronics 2018年第1期29卷 39-47页

作者： WANG Qian ZHANG Chuanding XIAN Deyong Beijing Satellite Navigation Center Beijing 100094China

Traditional global navigation satellite system(GNSS)terminals for satellite navigation adopt independent channels to track the signals from different satellites, which results in a lack of information interaction between the channels. Inspired by the vector tracking idea, and drawing lessons from the principle that in the position domain the Taylor expanded pseudorange observations can be used for positioning via the least squares method, this paper proposes a novel least squares-based multi-channel parameter joint estimation(MPJE) method in the signal domain, which not only retains the advantages of channel fusion, but also maintains the flexibility and diversity of the localization algorithm. With achieving optimal carrier to noise ratio as the goal, the proposed method obtains the required code loop and carrier loop parameters for signal tracking in the domain of whole channels. Experimental results indicate that this method fully achieves the assistant fusion advantages of frequency lock loop(FLL), phase lock loop(PLL)and delay lock loop(DLL), making good use of the robustness and dynamic properties of the FLL and the measurement accuracy of the DLL, and is helpful for achieving stable and accurate signal tracking under weak signals and high dynamic stress environments.

关键词： least squares method signal parameter optimization vector tracking global navigation satellite system(GNSS) weight matrix

least squares Evaluations for Form and Profile Errors of Ellipse Using Coordinate Data

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Chinese Journal of Mechanical Engineering 2016年第5期29卷 1020-1028页

作者： LIU Fei XU Guanghua LIANG Lin ZHANG Qing LIU Dan School of Mechanical Engineering Xi'an Jiaotong University State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System Xi'an Jiaotong University

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.

关键词： ellipse form Error profile error least squares method piston