Least-squares Estimation Method Research Articles

Current Distribution Reconstruction in Low-Voltage Circuit Breakers Based on Magnetic Inverse Problem Solution Considering Ferromagnetic Splitters

Current density distribution in electric arcs inside low-voltage circuit breakers (LVCBs) is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic field. This paper is focused on the modeling and computational phase for the magnetic inverse problem when linear ferromagnetic regions are considered in the model. To address the ill-posedness of the inverse problem, the standard method of least-squares approximation by Tikhonov regularization is studied, complemented with the generalized cross-validation criterion for regularization parameter selection. Considering the inclusion of a ferromagnetic region, two regularization approaches have been analyzed for the formulation of the currents in splitters and their corresponding magnetic field contribution. Effects of several features on the performance of the regularized solution have been investigated, including the signal-to-noise ratio, the value of permeability of the splitters, and the measurement distance. The numerical tests show the direct accessibility for the 3-D current density distribution with the proposed scheme, providing the accuracy and robustness for the applicability to study the arc behavior in LVCBs.

Peak-to-average power ratio reduction for DCO-OFDM underwater optical wireless communication system based on an interleaving technique

In underwater direct current-biased optical orthogonal frequency-division multiplexing (DCO-OFDM) system, high peak-to-average power ratio (PAPR) brings in-band distortion and out-of-band power. It also decreases the signal-to-quantization noise ratio of the analog-to-digital converter and the digital-to-analog converter. A time–frequency-domain interleaved subbanding scheme is proposed to reduce the PAPR of underwater DCO-OFDM system with low computation complexity and bit error rate (BER). The system BER is evaluated by the distances of the underwater optical wireless communication (UOWC), as well as by the signal attenuation of the UOWC channel. A least-square channel estimation method is adopted for adaptive power amplification at the receiver side, to further decrease the system BER.

Ranging Optimization and Research on Indoor 3D Positioning Algorithm Based on UWB

Nowadays, the indoor space of people is more and more vast and complex, so the service of positioning and guidance in parking lots, shopping malls, and airport is increasingly needed. Thus, especially indoor 3D positioning, IPS(Indoor Positioning System) has the chance to develop rapidly. This paper proposed UWB as the indoor 3D positioning technology and developed a method to improve TWR(tow-way-ranging) algorithm to enhance the precision of indoor 3D positioning. Furthermore, a 3D positioning algorithm based on TOF ranging with the LSE (Least Squares Estimation) method is introduced. Lastly, the simulation results in Matlab are showed to prove that this algorithm can achieve a relatively accurate 3D positioning precision, which is meaningful and practical for many applications.

Posterior distributions, sampling distributions and inter-laboratory comparison data

Weighted least-squares estimation methods are often used in the analysis of inter-laboratory comparison data. In classical statistics, least-squares methods can be justified in terms of properties of sampling distributions. However, not all distributions associated with laboratory results can be regarded sampling distributions and, for these cases, least-squares methods are a less straightforward to justify. Furthermore, they can give results that differ significantly from a Bayesian analysis. We illustrate these differences for the case in which the results of the laboratories are derived from repeated measurements.

Computational explosion in the frequency estimation of sinusoidal data

This paper highlights the computational explosion issues in the autoregressive moving average approach of frequency estimation of sinusoidal data with a large sample size. A new algorithm is proposed to circumvent the computational explosion difficulty in the conditional least-square estimation method. Notice that sinusoidal pattern can be generated by a non-invertible non-stationary autoregressive moving average (ARMA) model. The computational explosion is shown to be closely related to the non-invertibility of the equivalent ARMA model. Simulation studies illustrate the computational explosion phenomenon and show that the proposed algorithm can efficiently overcome computational explosion difficulty. Real data example of sunspot number is provided to illustrate the application of the proposed algorithm to the time series data exhibiting sinusoidal pattern.

Different estimation methods for exponentiated Rayleigh distribution under constant‐stress accelerated life test

AbstractThe accelerated life testing is an efficient approach and has been used in several fields to obtain failure time data of test units in a much shorter time than testing at normal operating conditions. In this article, we consider 6 frequentist estimation methods, namely, method of maximum likelihood estimation, method of least square estimation, method of weighted least square estimation, method of percentile estimation, method of maximum product of spacing estimation, and method of Cramér‐von‐Mises estimation to estimate the parameters and the reliability function of the exponentiated Rayleigh distribution under normal use conditions using constant accelerated life testing. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their mean squared error using simulated samples. Simulation results showed that percentile method gives the best results among other estimation methods in terms of mean squared error. Finally, a real data set is analyzed for illustrative purposes.

A reliable algorithm based on the shifted orthonormal Bernstein polynomials for solving Volterra–Fredholm integral equations

ABSTRACTThis paper deals with the numerical solution of Volterra–Fredholm integral equations. In this work, we approximate the unknown functions based on the shifted orthonormal Bernstein polynomials, in conjunction with the least-squares approximation method. The method is using a simple computational manner to obtain a quite acceptable approximate solution. The merits of this method lie in the fact that, on the one hand, the problem will be reduced to a system of algebraic equations. On the other hand, the efficiency and accuracy of the method for solving these equations are high. The convergence analysis of proposed method have been discussed through some theorems. Moreover, we will obtain an estimation of error bound for this algorithm. Finally, some examples are given to show the capability of presented method in comparison with four well-known algorithms in the literature namely the Legendre collocation method, Taylor collocation method, Taylor polynomial method and Lagrange collocation method.

Technical Efficiency-Minimum Absolute Deviation and Corrected Least Squares Methods of Estimation

Technical Efficiency-Minimum Absolute Deviation and Corrected Least Squares Methods of Estimation

Network Identification With Latent Nodes via Autoregressive Models

We consider linear time-invariant networks with unknown topology where only a manifest subset of the nodes can be directly actuated and measured while the state of the remaining latent nodes and their number are unknown. Our goal is to identify the transfer function of the manifest subnetwork and determine whether interactions between manifest nodes are direct or mediated by latent nodes. We show that if there are no inputs to the latent nodes, the manifest transfer function can be approximated arbitrarily well in the $H_{\infty }$ -norm sense by the transfer function of an autoregressive model and present a least-squares estimation method to construct the autoregressive model from measured data. We show that the least-squares autoregressive method guarantees an arbitrarily small $H_{\infty}$ -norm error in the approximation of the manifest transfer function, exponentially decaying once the model order exceeds a certain threshold. Finally, we show that when the latent subnetwork is acyclic, the proposed method achieves perfect identification of the manifest transfer function above a specific model order as the length of the data increases. Various examples illustrate our results.

Density forecasting of daily electricity demand with ARMA-GARCH, CAViaR, and CARE econometric models

Abstract The emerging need for risk-aware operational decisions on power systems calls for the development of accurate probabilistic load forecasting methods. To serve this purpose, various celebrated modeling approaches are applied from the field of economics where uncertainty forecasting has been a longstanding fundamental area of research. In particular, this paper proposes the use of ARMA-GARCH conditional mean–variance model in day-ahead forecasting and evaluates the CAViaR quantile regression model and the CARE expectile regression model as alternatives, with all of them incorporating exogenous inputs. In addition to the conventional quasi-maximum likelihood estimation (QMLE) of the ARMA-GARCH model, a special emphasis is put on least-squares (LS) based iterative and nonlinear estimation schemes. Empirical results are generated based on low-voltage side currents collected from transformers in the Netherlands, with the forecasts being assessed probabilistically via the continuous ranked probability score. Performance comparisons demonstrated improved results with the ARMA-GARCH model in relation to the others. Moreover, its estimation by means of the proposed iterative LS estimation method achieved the best forecast performance in a short runtime, thereby proven to be attractive for practical deployment.

Optimal and Suboptimal Velocity Estimators for ArcSAR With Distributed Target

Two new methods of radial velocity estimation for distributed targets in arc-scanning synthetic aperture radar (ArcSAR) systems, namely, the maximum-likelihood estimator (MLE) and the suboptimal method based on the least squares estimation (LSE), are proposed, derived, and analyzed. To this end, we establish that $n$ scatterers of the distributed target are uniformly dispersed within the radar resolution cell of dimensions $a \times b$ and they move randomly at different velocities. Furthermore, the effect of the antenna pattern is considered to characterize the amplitude of the scattered signal. Thus, from the coherent integration of the scatters at each pulse repetition interval in radar scanning, $m$ data sequences are obtained as samples of the composite signal, which follows a multivariate normal distribution. From this, the covariance matrix, upon which the methods are based, is derived. Simulations have been carried out to compare the new methods with existing methods, namely, phase, energy, and correlation, as a function of the signal-to-noise ratio. Finally, the results show that the MLE and LSE methods outperform the conventional methods, providing a gain of more than 10 dB.

Least Squares Estimation Based SDP Cuts for SOCP Relaxation of AC OPF

This paper presents a method that generates affine inequalities to strengthen the second-order conic programming (SOCP) relaxation of an alternating current optimal power flow (AC OPF) problem. The affine inequalities serve as cuts to get rid of points outside of the feasible region of AC OPF with semi-definite programming (SDP) relaxation. Hence, the affine inequalities are names as SDP cuts. While AC OPF with SDP relaxation has a high computational complexity, AC OPF with SOCP has a much lower computational complexity. Recent research has found that the feasible region of SDP relaxation is contained inside the feasible region of the SOCP relaxation. Therefore, the integration of SDP cuts into SOCP relaxation provides better scalability compared to the SDP relaxation and a tighter gap compared to the SOCP relaxation. The SDP cuts are generated by solving least square estimation (LSE) problems at cycle basis and further exploring the geometric characteristic of LSE. General feasibility cuts generating method is also employed for analysis. We found that the SDP cuts generated by LSE method are indeed feasibility cuts. The SDP cuts effectively reduce the search space. Case studies of systems with several buses to hundreds of buses have demonstrated the method is very effective in reducing the gaps.

Online Path Planning of Autonomous UAVs for Bearing-Only Standoff Multi-Target Following in Threat Environment

The problem of steering multiple fixed-wing autonomous unmanned aerial vehicles (UAVs) to follow the multiple noncooperative and high agile surface targets at a specified standoff distance in a threat environment is studied. Two kinds of threats and missed detection of bearing-only sensors are considered. The average nonlinear least-square estimation method is proposed to acquire the position of the targets using noisy measurements, and then, the trajectories of the targets are approximated by the quadratic functions of time. Dummy targets of the same number as UAVs are created according to the task allocation result to achieve the optimal geometric configuration of the multiple cooperative UAVs. And a case-based guidance method is established to finally accomplish the multi-target standoff following mission on-line. Simulation experiments are given to assess the proposed method.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate

PurposeTo describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. MethodsParameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. ResultsThe simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. ConclusionThe VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method.

Financial Inclusion under Internet Plus and Household Entrepreneurial Decisions

By using the data of China Family Panel Studies 2014, this paper investigates the effect of financial inclusion under Internet Plus on household entrepreneurial decisions from two perspectives of width and depth based on discrete variables selection model and two-stage least-squares estimation method. It arrives at the following conclusions:through the fusion of the information flow and the financing flow, the fusion of Internet Plus and financial inclusion reduces the risks in household business financing and increases its participation in formal financial market, thereby promoting ordinary household entrepreneurial probability; especially in urban families, high income families and families at higher education level, it plays a significantly promotion role in their entrepreneurial decisions; besides, the fusion of Internet Plus and financial inclusion also makes families be more active in opportunity-based entrepreneurial activities. This paper validates the availability of the effects of financial inclusion under Internet Plus on formal financial financing preference and risk preference channels in household entrepreneurial decisions, which is of great significance to the improvement of financial supportive environment in present work of popular entrepreneurship and innovation.

Do Social Responsibility and Social Media Dance together in Building Employer Reputation? Yes

This study theorizes that firms engaging in socially responsible activities are more likely to be perceived as a more attractive employer, and that this positive relationship may be amplified if firms have proficiency in leveraging social media platforms. This potential amplifier role may be explained through the greater social visibility enabled by social media. The proposed theory is tested using the structural equation modeling technique and the partial least squares method of estimation employing a secondary dataset on a sample composed of 100 large Spanish firms included in the Actualidad Economica’s Great Place to Work 2015. The empirical analysis supports our theory. This paper contributes to Information Systems research by theorizing and empirically demonstrating that social media capability creates business value by maximizing the positive impact of firm’s implementation of corporate social responsibility activities on the building of firm’s employer reputation.

A model for the interaction of phytoplankton aggregates and the environment: approximation and parameter estimation

We present a model for the dynamics of phytoplankton aggregates and their interaction with the environment in a well-mixed reactor or surface layer of a water column. The biophysical problem yields a nonlinear partial differential equation coupled with a general system of ordinary differential equations. We first develop a finite difference scheme for approximating the solution of this model. Then convergence results are established for the finite difference method and existence-uniqueness of solutions are obtained. A least-squares parameter estimation method is presented to illustrate the performance of the model against a real dataset, and to highlight the effects of aggregate growth on algal bloom dynamics and nutrient consumption rates. The model is well-suited to complement microcosm studies and can accommodate the effects of a wide range of environmental conditions.

A New Extension of Generalized Exponential Distribution with Application to Ozone Data

ABSTRACTIn this article, a new distribution, called transformed Generalized Exponential Distribution () is proposed. The distribution has simple closed forms pdf and cdf. Several properties of the distribution are studied including unimodality, moments, conditional moments, stochastic ordering and Shannon entropy. The distribution is capable of monotonically increasing, decreasing, bathtub and upside down shaped hazard rates. Furthermore, we discussed several methods of estimation for estimating the parameters. In particular, we compare, through simulation study, the performance of the maximum likelihood estimation, maximum product spacing estimation, ordinary and weighted least-squares estimation methods. Also, the average interval lengths and coverage rates of 95% confidence intervals, including boot-p and boot-t confidence intervals for different parameter values are provided. A real data set is used to illustrate the applicability of the proposed distribution.

Numerical studies on the effect of measurement noises on the online parametric identification of a cable-stayed bridge

System identification of structures is one of the important aspects of structural health monitoring. The accuracy and efficiency of identification results is affected severely by measurement noises, especially when the structure system is large, such as bridge structures, and when online system identification is required. In this paper, the least square estimation (LSE) method is used combined with the substructure approach for identifying structural parameters of a cable-stay bridge with large degree of freedoms online. Numerical analysis is carried out by first dividing the bridge structure into smaller substructures and then estimates the parameters of each substructure online using LSE method. Simulation results demonstrate that the proposed approach is capable of identifying structural parameters, however, the accuracy and efficiency of identification results depend highly on the noise sensitivities of loading region, loading pattern as well as element size.

Direct Linear System Identification Method for Multistory Three-dimensional Building Structure with General Eccentricity

A method of physical-parameter system identification is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time-domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. While previous researches on the system identification of 3D building structures are limited to a class of structures with regular eccentricity, the present paper removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.