WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

GPS short-delay multipath estimation and mitigation based on least square method

The GPS multipath signal model is presented, which indicates that the coherent DLL outputs in multipath environment are the convolution between the ideal DLL outputs and the channel responses. So the channel responses can be estimated by a least square method using the observed curve of the DLL discriminator. In terms of the estimated multipath channels, two multipath mitigation methods are discussed, which are equalization filtering and multipath subtracting, respectively. It is shown, by computer simulation, that the least square method has a good performance in channels estimation and the multipath errors can be mitigated almost completely by either of the methods. However, the multipath subtracting method has relative small remnant errors than equalization filtering.

Recursive Least Square Vehicle Mass Estimation Based on Acceleration Partition

Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method （RLSM） schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.

Study on least square modeling of heat engineering object based on typical signal response

This paper proposes a kind of least square modeling method based on typical signal response to enhance modeling accuracy of heat engineering process and adapts the environment that modeling experiment conditions are limited. The principle of this method is, under the condition of known typical pulse, step and slope signal response and model structure, to give algorithm of model parameters of identified continuous system by least square mode through derivation. The method is applied to the identification of heat exchange process for a consumer substation, and identification result obtained is compared with that of other conventional methods. After the comparison the result shows that identification accuracy is improved obviously. In addition to the good identification accuracy, this method has the characteristics such as it can identify directly continuous system model, pure lagging time, and is not sensitive to data length in the identification process. All these characteristics show that this method is simple, easy to implement and has good practicability.

Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.

The least square particle finite element method for simulating large amplitude sloshing flows

Large amplitude sloshing in tanks is simulated by the least square particle finite element method （LSPFEM） in this paper. The least square finite element method （LSFEM） is employed to spatially discrete the Navier-Stokes equations, and to avoid the stabilization issues due to the incompressibility condition for equal-order interpolation of the velocity and the pressure, as usually used in Galerkin method to satisfy the well-known LBB condition. The LSPFEM also uses the Lagrangian description to model the motion of nodes （particles）. A mesh which connects these nodes is constructed by a triangulation algorithm to avoid the mesh distortion. A quasi a-shapes algorithm is used to identify the free surface boundary. The nodes are viewed as particles which can freely move and even separate from the main fluid domain. Finally this method is used to study the large amplitude sloshing evolution in two dimensional tanks. The results are compared with those obtained by Flow-3d with good agreement.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

Application of neural network model coupling with the partial least-squares method for forecasting watre yield of mine

Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.

NON-PARAMETRIC LEAST SQUARE ESTIMATION OF DISTRIBUTION FUNCTION

By using the non parametric least square method, the strong consistent estimations of distribution function and failure function are established,where the distribution function F(x) after logist transformation is assumed to be approximated by a polynomial.The performance of simulation shows that the estimations are highly satisfactory.

Prediction of Logistics Demand via Least Square Method and Multi-Layer Perceptron

To implement the prediction of the logistics demand capacity of a certain region,a comprehensive index system is constructed,which is composed of freight volume and other eight relevant economic indices,such as gross domestic product(GDP),consumer price index(CPI),total import and export volume,port's cargo throughput,total retail sales of consumer goods,total fixed asset investment,highway mileage,and resident population,to form the foundation for the model calculation.Based on the least square method(LSM)to fit the parameters,the study obtains an accurate mathematical model and predicts the changes of each index in the next five years.Using artificial intelligence software,the research establishes the logistics demand model of multi-layer perceptron(MLP)neural network,makes an empirical analysis on the logistics demand of Quanzhou City,and predicts its logistics demand in the next five years,which provides some references for formulating logistics planning and development strategy.

Recursion Least Square Method to Study the Fault Diagnosis and Its Model of Hydraulic Equipment

In this paper establishing model of the fault diagnosis of hydraulic equipment isdescribed in details. It also studies the advantage of the recursion least square method. When theLSM is used in compuring the fault of hydraulic equipment, not only does it save the computerCPU-time and memory, but it also has a high computation speed and,makes it easy to identifythe estimation parameters.

Viscous flow with free surface motion by least square finite element method

A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

MULTI-RESOLUTION LEAST SQUARES SUPPORT VECTOR MACHINES

The Least Squares Support Vector Machines (LS-SVM) is an improvement to the SVM. Combined the LS-SVM with the Multi-Resolution Analysis (MRA),this letter proposes the Multi-resolution LS-SVM (MLS-SVM).The proposed algorithm has the same theoretical framework as MRA but with better approximation ability.At a fixed scale MLS-SVM is a classical LS-SVM,but MLS-SVM can gradually approximate the target function at different scales.In experiments,the MLS-SVM is used for nonlinear system identification,and achieves better identification accuracy.

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.

A LEAST SQUARE BASED WEAK GALERKIN FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC EQUATIONS IN NON-DIVERGENCE FORM

This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system is symmetric and positive definite,and thus the algorithm is easy to implement and analyze.Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular polygonal mesh.A superconvergence result is proved when the coefficient matrix is constant or piecewise constant.Numerical examples are performed which not only verify the theoretical results but also reveal some unexpected superconvergence phenomena.

Mixed Least Square Method for Priority of Complementary Judgement Matrix and Its Algorithm

Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.

Constant Stress Accelerated Life Tests for Vacuum Fluorescent Display Based on Least Square Method

To estimate the life of vacuum fluorescent display （VFD） more accurately and reduce test time and cost, four constant stress accelerated life tests （CSALTs） were conducted on an accelerated life test model. In the model, statistical analysis of test data is achieved by applying lognormal function to describe the life distribution, and least square method （LSM） to calculate the mean value and the standard deviation of logarithm. As a result, the accelerated life equation was obtained, and then a self-developed software was developed to predict the VFD life. The data analysis results demonstrate that the VFD life submits to lognormal distribution, that the accelerated model meets the linear Arrhenius equation, and that the precise accelerated parameter makes it possible to acquire the life information of VFD within one month.