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.

Consistency and Asymptotic Property of a Weighted Least Squares Method for Networked Control Systems

In this paper, we study the problems related to parameter estimation of a single-input and single-output networked control system, which contains possible network-induced delays and packet dropout in both of sensor-to-controller path and controller-to-actuator path. A weighted least squares(WLS) method is designed to estimate the parameters of plant, which could overcome the data uncertainty problem caused by delays and dropout. This WLS method is proved to be consistent and has a good asymptotic property. Simulation examples are given to validate the results.

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.

NEW RESULTS ABOUT THE RELATIONSHIP BETWEEN OPTIMALLY WEIGHTED LEAST SQUARES ESTIMATE AND LINEAR MINIMUM VARIANCE ESTIMATE

The optimally weighted least squares estimate and the linear minimum variance estimateare two of the most popular estimation methods for a linear model.In this paper,the authors makea comprehensive discussion about the relationship between the two estimates.Firstly,the authorsconsider the classical linear model in which the coefficient matrix of the linear model is deterministic,and the necessary and sufficient condition for equivalence of the two estimates is derived.Moreover,under certain conditions on variance matrix invertibility,the two estimates can be identical providedthat they use the same a priori information of the parameter being estimated.Secondly,the authorsconsider the linear model with random coefficient matrix which is called the extended linear model;under certain conditions on variance matrix invertibility,it is proved that the former outperforms thelatter when using the same a priori information of the parameter.

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.

Effects of errors-in-variables on the internal and external reliability measures

The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.

Overlapped peaks resolution for linear sweep polarography using Gaussian-like distribution

A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.

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.

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.

Multiple Excitation Wavelength Fluorescence Emission Spectra Technique for Discrimination of Phytoplankton

In vivo fluorescence methods are efficient tools for studying the distribution of phytoplankton in nature.Different algae species usually have different pigments with different ratios,which results in different fluorescence emission spectra.Based on multiple excitation wavelength fluorescence emission spectra,a discrimination technique is established in this study.The discrimination method,established by multivariate linear regression and weighted least-squares,was used to differentiate the samples cultured in the laboratory and collected from Jiaozhou Bay near Qingdao at the division level.The correctly discriminated samples were ≥ 86% for single algae samples,≥ 88% for simulatively mixed ones,≥ 91% for physically mixed ones and 100% for samples collected from Jiaozhou Bay.The result in this research is more definite for the physically mixed samples in the laboratory.The method described here can be employed to monitor the phytoplankton population in the marine environment.

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.