Least Square Inversed Analysis of Soil Parameter for Foundation with Two-Order Gradient Theoretic Method

2011 ◽  
Vol 243-249 ◽  
pp. 2294-2299 ◽  
Author(s):  
Yao Feng Xie
Keyword(s):  
Differential Equations ◽  
Error Function ◽  
Least Square Method ◽  
Least Square ◽  
Gradient Theory ◽  
Mechanical Theory ◽  
Soil Parameter ◽  
True Value ◽  
Initial Soil ◽  
Calculation Results

Combined with two-order gradient theory, the least square inversed analysis of the soil parameter for the foundation is studied and put forward in detail. After the mechanical theory for the plate on the foundation is introduced, the controlling differential equations of the plate on the foundation which is subjected to vertical loads are deduced. Through utilizing Fourier transformative theory, the corresponding solutions to the plate on the foundation are gained. Linear algebra controlling equations for the plate are achieved which leads to solve the original differential equations more easily. The least square error function for the soil parameter on the plate is established and applied with the two-order gradient method. The inversed steps on the least square error function for the soil parameter are listed. The calculation results verify the conclusions that the soil parameter of the foundation can be efficiently inversed by applying the least square theory. When different initial soil parameter is set, the iterative computations can be convergent to the true value of the soil parameter. And this least square method can also be applied for the problem of inversed analysis of parameters for other foundation models.

Analysis of the Mindlin Plate and Identification of the Soil Parameter for Foundation with Gradient Optimizing Method

2012 ◽  
Vol 256-259 ◽  
pp. 3-10
Author(s):  
Tao Hong ◽  
Mei Jun Lu ◽  
Chu Wei Zhou ◽  
Jian Zhang
Keyword(s):  
Differential Equations ◽  
Error Function ◽  
Mindlin Plate ◽  
Mechanical Theory ◽  
Soil Parameter ◽  
True Value ◽  
Initial Soil ◽  
Calculation Results ◽  
Identification Analysis ◽  
Markov Method

Analysis of Mindlin plate is completed. And combined with gradient optimizing method, the Gaussian Markov identification analysis of the soil parameter for the foundation is studied and put forward in detail. After the mechanical theory for the plate on the foundation is introduced, the controlling differential equations of the plate on the foundation which is subjected to vertical loads are deduced. And linear algebra controlling equations for the plate are achieved which leads to solve the original differential equations more easily when the corresponding solutions to the plate on the foundation are gained with Fourier transformative theory. The Gaussian Markov error function for the soil parameter on the plate is established and applied with the gradient optimizing method. The identification steps on the Gaussian Markov error function for the soil parameter are listed. The calculation results verify the conclusions that the soil parameter of the foundation can be efficiently inversed by applying the Gaussian Markov theory. When different initial soil parameter is set, the iterative computations can be convergent to the true value of the soil parameter. And this Gaussian Markov method can also be applied for the problem of inversed analysis of parameters for other foundation models.

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

scholarly journals Calculation and realization of new method grey residual error correction model

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254154
Author(s):  
Lifang Xiao ◽  
Xiangyang Chen ◽  
Hao Wang
Keyword(s):  
Prediction Model ◽  
Least Square Method ◽  
Residual Error ◽  
Least Square ◽  
Grey Model ◽  
Grey Prediction ◽  
Grey Prediction Model ◽  
True Value ◽  
Prediction Function ◽  
Fitting Method

Aiming at the problem of prediction accuracy of stochastic volatility series, this paper proposes a method to optimize the grey model(GM(1,1)) from the perspective of residual error. In this study, a new fitting method is firstly used, which combines the wavelet function basis and the least square method to fit the residual data of the true value and the predicted value of the grey model(GM(1,1)). The residual prediction function is constructed by using the fitting method. Then, the prediction function of the grey model(GM(1,1)) is modified by the residual prediction function. Finally, an example of the wavelet residual-corrected grey prediction model (WGM) is obtained. The test results show that the fitting accuracy of the wavelet residual-corrected grey prediction model has irreplaceable advantages.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Calculation of ICG kinetics by two simultaneous differential equations and non-linear least square method.

Kanzo ◽  
1988 ◽  
Vol 29 (10) ◽  
pp. 1368-1373
Author(s):  
Yutaka SAGAWA ◽  
Toshiko YOSHIKATA ◽  
Nagaki SHIMADA ◽  
Motonobu SUGIMOTO
Keyword(s):  
Differential Equations ◽  
Least Square Method ◽  
Least Square ◽  
Non Linear ◽  
Linear Least Square

Identification and Compensation of a Robot Kinematic Parameter for Positioning Accuracy Improvement

Robotica ◽  
1991 ◽  
Vol 9 (1) ◽  
pp. 99-105 ◽  
Author(s):  
D. H. Kim ◽  
K. H. Cook ◽  
J. H. Oh
Keyword(s):  
Error Function ◽  
Least Square Method ◽  
Kinematic Parameter ◽  
Least Square ◽  
Joint Angles ◽  
Kinematic Parameters ◽  
Accuracy Improvement ◽  
Coordinate Frames ◽  
Identification Method ◽  
Value Decomposition

SUMMARYThis paper presents a simple identification method of the actual kinematic parameters for a robot with parallel joints. It is known that Denavit–Hartenberg's coordinate System is not useful for nearly parallel joints. In this paper, the coordinate frames are reassigned to model the kinematic parameter between nearly parallel joints by four parameters. The proposed identification method uses a straight ruler about 1 m long. A robot hand is placed by using a teaching pendant at the prescribed points on the ruler, and the corresponding error function is defined. The identified kinematic parameters, which make the error function zero, are obtained by the iterative least square method based on the singular value decomposition. In the compensation of joint angles, only the position is considered because the usual applications of robot do not require a precise orientation control.

scholarly journals Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method

2020 ◽  
Vol 33 (4) ◽  
pp. 59
Author(s):  
Israa M. Salman ◽  
Eman A. Abdul-Razzaq
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

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