Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Modeling Solid Waste Minimization Performance at Source in Dar es Salaam City, Tanzania

Municipal solid waste generation is strongly linked to rising human population and expanding urban areas, with significant implications on urban metabolism as well as space and place values redefinition. Effective management performance of municipal solid waste management underscores the interdisciplinarity strategies. Such knowledge and skills are paramount to uncover the sources of waste generation as well as means of waste storage, collection, recycling, transportation, handling/treatment, disposal, and monitoring. This study was conducted in Dar es Salaam city. Driven by the curiosity model of the solid waste minimization performance at source, study data was collected using focus group discussion techniques to ward-level local government officers, which was triangulated with literature and documentary review. The main themes of the FGD were situational factors (SFA) and local government by-laws (LGBY). In the FGD session, sub-themes of SFA tricked to understand how MSW minimization is related to the presence and effect of services such as land use planning, availability of landfills, solid waste transfer stations, material recovery facilities, incinerators, solid waste collection bins, solid waste trucks, solid waste management budget and solid waste collection agents. Similarly, FGD on LGBY was extended by sub-themes such as contents of the by-law, community awareness of the by-law, and by-law enforcement mechanisms. While data preparation applied an analytical hierarchy process, data analysis applied an ordinary least square (OLS) regression model for sub-criteria that explain SFA and LGBY;and OLS standard residues as variables into geographically weighted regression with a resolution of 241 × 241 meter in ArcMap v10.5. Results showed that situational factors and local government by-laws have a strong relationship with the rate of minimizing solid waste dumping in water bodies (local R square = 0.94).

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

基于PCA-OLS模型的系统等效惯量中长期预测

为综合考虑多重影响因素与系统等效惯量之间的量化关系,本文提出一种基于主成分分析-普通最小二乘法的系统等效惯量中长期预测模型。根据电网实际调度规则搭建简化的开机方式优化模型,构建系统等效惯量中长期预测历史数据集;利用主成分分析对系统等效惯量主要影响因素的多重共线性进行消除,得到主成分表达式;进行多元普通最小二乘法回归,反标准化后得到系统等效惯量解析模型。根据某电网能源发展规划数据,对未来系统惯量水平进行推演,可快速预估不同运行方式下系统等效惯量的演化趋势及非同步电源承载能力。

基于OLS+GWR模型的非粮化利用方式对耕地质量的影响

为探究不同非粮化利用方式对耕地质量的影响,基于最小二乘法线性回归(OLS)模型和地理加权回归(GER)模型对海南省儋州市部分地区非粮化耕地影响空间分布进行分析。结果表明,研究区采用景观苗木种植方式时,对中西部土壤有机质含量、东南和西南土壤pH值、东南地区面积加权形状指数影响较大,景观苗木种植方式是这3项指标的关键影响因素;研究区采用果树种植方式时,对于东部和西部地区土壤有机质含量、西部地区土壤破碎指数、东南和西南部分地区面积加权形状指数影响较大,果树种植方式是这3项指标的关键影响因素;研究区采用草坪种植方式时,对研究区东部地区破碎化指数和种植规模的影响较大,草坪种植是这2项指标的关键影响因素;研究区采用挖塘养殖方式时,对中部、西北和西南地区的土壤pH值、东南部分地区种植规模影响较大,挖塘养殖是这2项指标的关键影响因素。

An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target

A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

Penalized total least squares method for dealing with systematic errors in partial EIV model and its precision estimation

When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT (Ⅰ)-VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant ver- tical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.

Numerical simulation of flow around square cylinder using different low-Reynolds number turbulence models

ABE-KONDOH-NAGANO,ABID,YANG-SHIH and LAUNDER-SHARMA low-Reynolds number turbulence models were applied to simulating unsteady turbulence flow around a square cylinder in different phases flow field and time-averaged unsteady flow field.Meanwhile,drag and lift coefficients of the four different low-Reynolds number turbulence models were analyzed.The simulated results of YANG-SHIH model are close to the large eddy simulation results and experimental results,and they are significantly better than those of ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMR models.The modification of the generation of turbulence kinetic energy is the key factor to a successful simulation for YANG-SHIH model,while the correction of the turbulence near the wall has minor influence on the simulation results.For ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMA models satisfactory simulation results cannot be obtained due to lack of the modification of the generation of turbulence kinetic energy.With the joint force of wall function and the turbulence models with the adoption of corrected swirl stream,flow around a square cylinder can be fully simulated with less grids by the near-wall.

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.

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.

Factors influencing the internet banking adoption decision in North Cyprus: an evidence from the partial least square approach of the structural equation modeling

Purpose:This paper aims to examine how the adoption decision of the internet banking in North Cyprus would be affected based on the following dimensions;the technology features,the personal characteristics,the social environment and the expected risk.Design/methodology/approach:A self-administered survey was conducted with 291 participants responded to it.The partial least square approach of the structural equation modeling(PLS-SEM)is employed to investigate the direct effects of the proposed factors on the adoption decision.Additionally,the mediation test is used to examine indirect effects.Findings:Results showed that even though the participants appreciated the benefits of the online banking as the perceived usefulness factor exerts the greatest direct effect,they would rather use clear and easy-to-use websites,adding to that their assessments of the usefulness of these services are significantly influenced by the surrounding people’s views and prior experience.This is demonstrated by the total effects of the perceived ease of use and the subjective norm factors,which are greater than the direct effect of the perceived usefulness factor since both of these factors have significant direct and indirect effects mediated by the perceived usefulness factor.The negative impact of the perceived risk factor is weak compared to the previous factors.While the personal innovativeness factor showed the weakest effect among the proposed factors.

Prediction of the Local Scour at the Bridge Square Pier Using a 3D Numerical Model

In this paper, the problem on local scour around a single square pier was studied by using both the numerical and physical models. The numerical model for the study is FSUM based on a finite-difference method to solve the Reynolds averaged Navier-Stokes equations (RANS) and the equations for suspended sediment concentration and bed morphology. The computed result was verified through data measured in the experimental flume with a sand bed. In general, the typical features of local scour around the pier were successfully simulated by FSUM, such as stream flow, bow flow, down flow, horseshoe vortex. The comparison between the computation and experiment data shows a quite good fitness. Both numerical model and experiment results show that the maximum scour depth occurs at two front edges of the pier. Although the computed result shows a little bigger scour depth in comparison with the measurement in the physical model, it still confirms the reliability of numerical model in some measure.

Orthogonal-Least-Squares Forward Selection for Parsimonious Modelling from Data

The objective of modelling from data is not that the model simply fits the training data well. Rather, the goodness of a model is characterized by its generalization capability, interpretability and ease for knowledge extraction. All these desired properties depend crucially on the ability to construct appropriate parsimonious models by the modelling process, and a basic principle in practical nonlinear data modelling is the parsimonious principle of ensuring the smallest possible model that explains the training data. There exists a vast amount of works in the area of sparse modelling, and a widely adopted approach is based on the linear-in-the-parameters data modelling that include the radial basis function network, the neurofuzzy network and all the sparse kernel modelling techniques. A well tested strategy for parsimonious modelling from data is the orthogonal least squares (OLS) algorithm for forward selection modelling, which is capable of constructing sparse models that generalise well. This contribution continues this theme and provides a unified framework for sparse modelling from data that includes regression and classification, which belong to supervised learning, and probability density function estimation, which is an unsupervised learning problem. The OLS forward selection method based on the leave-one-out test criteria is presented within this unified data-modelling framework. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic parsimonious modelling approach from data.

Modified Two-Degrees-of-Freedom Internal Model Control for Non-Square Systems with Multiple Time Delays

A modified two-degrees-of-freedom( M-TDOF) internal model control( IMC) method is proposed for non-square systems with multiple time delays and right-half-plane( RHP) zeros. In this method,pseudo-inverse is introduced to design the internal model controller,and a desired closed-loop transfer function is designed to eliminate the unrealizable factors of the derived controller. In addition,set-point tracking and load-disturbance rejection of each process are separately controlled by two controllers. The simulation results show that in addition to high decoupling performance and robustness,the proposed control method also effectively improves loaddisturbance rejection and simultaneously optimizes the input tracking performance and disturbance rejection performance by selecting the parameters of controllers. Furthermore,the higher tolerance of model mismatch is achieved in this paper.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

Least squares fitting of coordinate parameters model

This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model. The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model. During discussion, the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.

A New Modified Conductivity Model for Prediction of Shear Yield Stress of Electrorheological Fluids Based on Face-center Square Structure

A new modified conductivity model was established to predict the shear yield stress of electrorheological fluids (ERF). By using a cell equivalent method, the present model can deal with the face-center square structure of ERF. Combining the scheme of the classical conductivity model for the single-chain structure, a new formula for the prediction of the shear yield stress of ERF was set up. The influences of the separation distance of the particles, the volume fraction of the particles and the applied electric field on the shear yield stress were investigated.