Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Constrained Weighted Least Squares Location Algorithm Using Received Signal Strength Measurements

Determine the location of a target has gained considerable interest over the past few years. The Received Signal Strength(RSS) measurements and Differential RSS(DRSS) measurements can be converted to distance or distance ratio estimates for constructing a set of linear equations. Based on these linear equations, a constrained weighted least Squares(CWLS) algorithm for target localization is derived. In addition, an iterative technique based on Newton's method is utilized to give a solution. The covariance and bias of the CWLS algorithm is derived using perturbation analysis. Simulation shows that the proposed estimator achieves better performance than existing algorithms with reasonable complexity.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

ON STABLE PERTURBATIONS OF THE STIFFLY WEIGHTED PSEUDOINVERSE AND WEIGHTED LEAST SQUARES PROBLEM

In this paper we study perturbations of the stiffly weighted pseudoinverse （W^1/2 A）^＋W^1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices A = A ＋ δA satisfy several row rank preserving conditions.

A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS

Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

Weighted Learning for Feedforward Neural Networks

In this paper, we propose two weighted learning methods for the construction of single hidden layer feedforward neural networks. Both methods incorporate weighted least squares. Our idea is to allow the training instances nearer to the query to offer bigger contributions to the estimated output. By minimizing the weighted mean square error function, optimal networks can be obtained. The results of a number of experiments demonstrate the effectiveness of our proposed methods.

Anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base

The performance of a strapdown inertial navigation system(SINS)largely depends on the accuracy and rapidness of the initial alignment.A novel anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base is presented in this paper.The algorithm transforms the initial alignment into the initial attitude determination problem by using infinite vector observations to remove the angular motions,the SINS alignment is heuristically established as an optimiza-tion problem of finding the minimum eigenvector.In order to further improve the alignment precision,an adaptive recursive weighted least squares(ARWLS)curve fitting algorithm is used to fit the translational motion interference-contaminated reference vectors according to their time domain characteristics.Simulation studies and experimental results favorably demonstrate its rapidness,accuracy and robustness.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

CHANNEL ERROR CORRECTION FOR WIDEBAND SAR-A JOINT MULTIPLE SUBPULSES PROCESSING METHOD

A novel method,referred to as joint multiple subpulses processing,is developed to calibrate the nonideal transfer function of radio frequency front-end and I/Q imbalance in quadrature modulate/demodulate systems simultaneously,which frequently occur in wideband Synthetic Aperture Radar(SAR) systems.Based on the time-frequency relation of the chirp signal and the analyses of the channel errors in wideband SAR,joint multiple subpulses processing method is adopted to separate the image frequency component due to the I/Q channel error.Then,the complete description of the channel error is acquired for building the correction function,which is used to correct the radar raw echo in frequency domain.The validity and capability of this method are demonstrated by the experiments of the channel error correction on the high resolution SAR system with the effective bandwidth of 500 MHz.

Influence of climatic conditions,topography and soil attributes on the spatial distribution of site productivity index of the species rich forests of Jalisco,Mexico

This paper presents an approach based on field data to model the spatial distribution of the site productivity index （SPI） of the diverse forest types in Jalisco, Mexico and the response in SPI to site and cli-matic conditions. A linear regression model was constructed to test the hypothesis that site and climate variables can be used to predict the SPI of the major forest types in Jalisco. SPI varied significantly with topog-raphy （elevation, aspect and slope）, soil attributes （pH, sand and silt）, climate （temperature and precipitation zones） and forest type. The most important variable in the model was forest type, which accounted for 35% of the variability in SPI. Temperature and precipitation accounted for 8 to 9% of the variability in SPI while the soil attributes accounted for less than 4% of the variability observed in SPI. No significant differences were detected between the observed and predicted SPI for the individual forest types. The linear regression model was used to develop maps of the spatial variability in predicted SPI for the individual forest types in the state. The spatial site productivity models developed in this study provides a basis for understanding the complex relationship that exists between forest productivity and site and climatic conditions in the state. Findings of this study will assist resource managers in making cost-effective decisions about the management of individual forest types in the state of Jalisco, Mexico.

Research on the discrimination methods of algae based on the fluorescence excitation spectra

The excitation spectra of chlorophyll （Chl） fluorescence can be used to differentiate phytoplankton populations at phylum level in vivo and in situ within a few minutes.The investigated phytoplankton divisions （Dinophyta,Bacillariophyta,Chrysophyta,Cyanophyta,Cryptophyta,Chlorophyta） are each characterized by a specific composition of photosynthetic antenna pigments and,consequently,by a specific excitation spectrum of the Chl fluorescence.Norm excitation spectra （emission of 680 nm and excitation of 400–600 nm） of every division were obtained from several species per division by a F4500 fluorescence spectrophotometer.Fisher’s linear discriminant analysis of the norm spectra shows that the divisions could be discriminated.The discrimination method,established by multivariate linear regression and weighted least squares,was used to differentiate the phytoplankton samples cultured in the laboratory and samples collected from the Jiaozhao Bay at division level.The correctly discriminated samples were more than 94% for single algal species ones,more than 84% for simulatively mixed ones,more than 83% for real mixed ones and 100% for samples collected from the Jiaozhou Bay for the dominant species.The method for phytoplankton differentiation described here can be applied to routine checking by fluorescence spectrophotometer,and benefit the monitoring and supervision tasks related to phytoplankton populations in the marine environments.

Power Inverted Topp–Leone Distribution in Acceptance Sampling Plans

We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.

Semidefinite programming approach for TDOA/GROA based source localization

Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.

Multilevel Modelling for Surgical Tool Calibration Using LINEX Loss Function

Quantifying the tool–tissue interaction forces in surgery can be utilized in the training of inexperienced surgeons,assist them better use surgical tools and avoid applying excessive pressures.The voltages read from strain gauges are used to approximate the unknown values of implemented forces.To this objective,the force-voltage connection must be quantified in order to evaluate the interaction forces during surgery.The progress of appropriate statistical learning approaches to describe the link between the genuine force applied on the tissue and numerous outputs obtained from sensors installed on surgical equipment is a key problem.In this study,different probabilistic approaches are used to evaluate the realized force on tissue using voltages read from strain gauges,including bootstrapping,Bayesian regression,weighted least squares regression,and multi-level modelling.Estimates from the proposed models are more precise than the maximum likelihood and restricted maximum likelihood techniques.The suggested methodologies are proficient of assessing tool-tissue interface forces with an adequate level of accuracy.

Concave Group Selection of Nonparameter Additive Accelerated Failure Time Model

In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.

The Most Sensitive Exchange Rates for Tin Based on the Major Commodity Production Countries

This paper examines the most sensitive exchange rates for tin price based on China and Indonesia that these are the world’s first and second largest tin producers.The export data from these countries have shared over 75 per cent of global tin supply that relates significantly with the Indonesian exchange rate based on the Canonical Correlation Analysis(CCA).Furthermore,the future tin prices are forecasted using the weighted least squares(WLS)model.This model is selected since it takes into account the non-normally distribution and heteroscedasticity of the original data.Overall,this result suggests that the Indonesian exchange rate is superior in predicting the future tin price rather than the Chinese exchange rate while China is the largest tin producer in the world.This is caused that the Chinese exchange rate cannot appreciate to other currency baskets.

Recursive Least Squares Estimator with Multiple Exponential Windows in Vector Autoregression

In the parameter tracking of time-varying systems, the ordinary method is weighted least squares with the rectangular window or the exponential window. In this paper we propose a new kind of sliding window called the multiple exponential window, and then use it to fit time-varying Gaussian vector autoregressive models. The asymptotic bias and covariance of the estimator of the parameter for time-invariant models are also derived. Simulation results show that the multiple exponential windows have better parameter tracking effect than rectangular windows and exponential ones.

An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

The improved element-free Galerkin method forthree-dimensional wave equation

The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.