Traditional Least-squares Method Research Articles

Construction and optimization of non-parametric analysis model for meter coefficients via back propagation neural network

This study addresses the drawbacks of traditional methods used in meter coefficient analysis, which are low accuracy and long processing time. A new method based on non-parametric analysis using the Back Propagation (BP) neural network is proposed to overcome these limitations. The study explores the classification and pattern recognition capabilities of the BP neural network by analyzing its non-parametric model and optimization methods. For model construction, the study uses the United Kingdom Domestic Appliance-Level Electricity dataset’s meter readings and related data for training and testing the proposed model. The non-parametric analysis model is used for data pre-processing, feature extraction, and normalization to obtain the training and testing datasets. Experimental tests compare the proposed non-parametric analysis model based on the BP neural network with the traditional Least Squares Method (LSM). The results demonstrate that the proposed model significantly improves the accuracy indicators such as mean absolute error (MAE) and mean relative error (MRE) when compared with the LSM method. The proposed model achieves an MAE of 0.025 and an MRE of 1.32% in the testing dataset, while the LSM method has an MAE of 0.043 and an MRE of 2.56% in the same dataset. Therefore, the proposed non-parametric analysis model based on the BP neural network can achieve higher accuracy in meter coefficient analysis when compared with the traditional LSM method. This study provides a novel non-parametric analysis method with practical reference value for the electricity industry in energy metering and load forecasting.

An Underwater Source Localization Method Using Bearing Measurements.

Angle-of-arrival (AOA) measurements are often used in underwater acoustical localization. Different from the traditional AOA model based on azimuth and elevation measurements, the AOA model studied in this paper uses bearing measurements. It is also often used in the Ultra-Short Baseline system (USBL). However, traditional acoustical localization needs additional range information. If the range information is unavailable, the closed-form solution is difficult to obtain only with bearing measurements. Thus, a localization closed-form solution using only bearing measurements is explored in this article. A pseudo-linear measurement model between the source position and the bearing measurements is derived, and considering the nonlinear relationship of the parameters, a weighted least-squares optimization equation based on multiple constraints is established. Different from the traditional two-step least-squares method, the semidefinite programming (SDP) method is designed to obtain the initial solution, and then a bias compensation method is proposed to further minimize localization errors based on the SDP result. Numerical simulations show that the performance of the proposed method can achieve Cramer-Rao lower bound (CRLB) accuracy. The field test also proves that the proposed method can locate the source position without range measurements and obtain the highest positioning accuracy.

Research on Temperature Compensation of Multi-Channel Pressure Scanner Based on an Improved Cuckoo Search Optimizing a BP Neural Network.

A multi-channel pressure scanner is an essential tool for measuring and acquiring various pressure parameters in aerospace applications. It is important to note, however, that the pressure sensor of each of these channels will drift significantly with the increase in the temperature range of the pressure measurement, and the output voltage of each of these channels will show nonlinear characteristics, which will constrain the improvements in the accuracy of the measurement. In the regression fitting process, it is difficult to fit nonlinear data with the traditional least-squares method, which leaves pressure measurement accuracy unsatisfactory. A temperature compensation method based on an improved cuckoo search optimizing a BP neural network for a multi-channel pressure scanner is proposed in this paper to improve pressure measurement accuracy in a wide temperature range. Using the chaotic simplex algorithm, we first improved the cuckoo search algorithm, then optimized the connection weights and thresholds of the BP neural network, and finally constructed an experimental calibration system to investigate the temperature compensation of the multi-channel pressure scanning valves in the −40 °C to 60 °C temperature range. The compensation test results show that the algorithm has a better compensation effect and is more suitable for the temperature compensation of multi-channel pressure scanners than the traditional least-squares method and the standard RBF and BP neural networks. The maximum full-scale error of all 32 channels is 0.02% FS (full-scale error) and below, which realizes its high-accuracy multi-point pressure measurement in a wide temperature range.

Discovery of new characterizations of parameter distributions in a semi- empirical mass model: an investigation by dividing an overdetermined system into numerous balanced subsystems* *Supported by the National Natural Science Foundation of China (11975209, U2032211, 12075287), the Physics Research and Development Program of Zhengzhou University (32410017), the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province (2017GGJS008)

We propose and test a new method of estimating the model parameters of the phenomenological Bethe-Weizsäcker mass formula. Based on the Monte Carlo sampling of a large dataset, we obtain, for the first time, a Cauchy-type parameter distribution formed by the exact solutions of linear equation systems. Using the maximum likelihood estimation, the location and scale parameters are evaluated. The estimated results are compared with those obtained by solving overdetermined systems, e.g., the solutions of the traditional least-squares method. Parameter correlations and uncertainty propagation are briefly discussed. As expected, it is also found that improvements in theoretical modeling (e.g., considering microscopic corrections) decrease the parameter and propagation uncertainties.

Design of Plane Wave Generator Based on Strong Robust Inverse Radiation Problem Solving Method

In this manuscript, we reconsider the amplitude and phase combination of the plane-wave generator (PWG) from an electromagnetic field inverse radiation perspective and further propose a new method based on the Gauss-Newton inversion (GNI) to perform the inverse design of PWG. Furthermore, the wideband antenna pattern is applied in the transfer function and makes the inversion results closer to the engineering implementation. Compared with the traditional least-squares method (LSM) and singular value decomposition (SVD) method, the proposed method owns the merits of less amplitude range of the input source and stronger robustness.

Application of random sample consensus method for parameter estimation of reflectometry density profile in toroidal plasma.

Microwave reflectometry diagnostics have been widely used to measure density profiles in fusion plasma. However, the high sensitivity of the diagnostics to plasma turbulence often results in large radial deviations in the edge density profile and causes difficulty in profile evaluation. To improve the performance of profile evaluation, a modified RANdom SAmple Consensus (RANSAC) method has been applied to fit the density profiles measured by reflectometry on the experimental advanced superconducting tokamak. Compared with the traditional least-squares method, the modified RANSAC method is much more efficient and robust in fitting the experimental profiles. Furthermore, a combination of RANSAC and a genetic algorithm (GA-RANSAC) is used to further optimize the profile evaluation procedure. The results show that this GA-RANSAC method yields better performance and stabler convergence than the modified RANSAC alone.

A Newly Designed Method for On-Line Error Estimation of Smart Meter

The method of manual verification of smart meters used at the current stage usually suffers from high cost, poor efficiency, and small coverage. A new method is presented to solve the error of energy meter by iteration. Firstly, the daily electricity data is collected and sifted through to classify the data for light-load and no-load meters. Then, by applying the outlier line-loss rate treatment method, it can obtain the invariable-loss & line-loss rate & the suspected out-of-tolerance meter and their initial values. After that, the meter error, invariable-loss, and line-loss rate can be calculated by the improved meter error estimation model. Based on the computed results, the data with relatively high and low line-loss rate are removed. It is to guarantee that the line-loss rate of data is within a small range. The sifted process removes the outliers and avoids the mis-deletion of the valid data, which improves the calculation accuracy. The proposed method proves to be effective in out-of-tolerance meter search by verifying the data from two different scale distribute-electricity transformer districts (DETDs) and comparing with the traditional least-squares method (LSM). The algorithm is easily applicable to small computation burdens.

Plasma optical emission spectroscopy based on feedforward neural network

Optical emission spectroscopy (OES) has been widely applied to plasma etching, material processing, development of plasma equipment and technology, as well as plasma propulsion. The collisional-radiative model used in OES is affected by the deviation of fundamental data such as collision cross sections, thus leading to the error in diagnostic results. In this work, a novel method is developed based on feedforward neural network for OES. By comparing the error characteristics of the new method with those of the traditional least-square diagnostic method, it is found that the neural network diagnosis method can reduce the transmission of basic data deviation to the diagnosis results by identifying the characteristics of the spectral vector. This is confirmed by the experimental results. Finally, the mechanism of the neural network algorithm against fundamental data deviation is analyzed. This method also has a good application prospect in plasma parameter online monitoring, imaging monitoring and mass data processing.

A Hybrid Steady-State Compressor Model for Real-Time Applications in Performance Monitoring, Control and Optimization

In this study, a hybrid steady-state compressor model is proposed that can be used in the real-time performance monitoring, control and optimization of the vapor compression cycle. In the proposed model, first, a detailed analysis of the mass flow rate is presented, which is based on the volumetric efficiency concept and the assumption of a polytropic compression process. Then, discharge temperature of the refrigerant and power consumption of the compressor are also investigated. Three semiempirical models are constructed respectively. Further, to tune the unknown empirical parameters of the models, a social learning particle swarm optimization (SLPSO) algorithm is developed by using the real-time experimental data. An experimental apparatus of a refrigerant system is tested to validate the proposed models. The experimental results demonstrate that the proposed models accurately predict the performance of real-time operating compressors. Meanwhile, the models identified by the SLPSO algorithm are more accurate than those identified by the traditional least-squares method.

Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases

This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation.

Parameter Identification Based on Nonlinear Observer for Mechanical Systems

Abstract This paper deals with the parameter identification problem for nonlinear mechanical systems based on state estimation. Here, the concept of Sliding Mode Observer for finite time state estimation and the Least-Square Method for parameter identification have been combined; thus, guaranteeing that the estimated state converges to the real one in a finite time. The asymptotic parameter identification is performed by applying the Least-Square approach, minimizing the so-called joint uncertainty; in this process, a specific persistent excitation condition is introduced to guarantee the effectiveness of the proposed identification algorithm. With the proposed approach and some considerations, the algorithm is capable of estimating friction coefficients and inertia moments, within a narrow time-window. Finally, the performance of the identification algorithm designed in this paper is tested on a real-time underactuated system, specifically the double pendulum on a cart platform. Furthermore, a successful benchmarking between the algorithm herein and the traditional least-square method is reported.

Iteratively reweighted total least squares for PEIV model

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems.

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

Phasor analysis of fluorescence lifetime data and its application

Fluorescence lifetime imaging microscopy (FLIM) is widely used in biomedical, materials and other fields. It not only has strong specificity and high sensitivity, but also has the capability of quantitative measurement because the fluorescence lifetime is not affected by the intensity of excitation, the concentration of fluorophores and photobleaching, and consequently is able to monitor the changes of microenvironment and reflecting the interaction between molecules. However, its application is limited to some extent by the complexity of data analysis. In order to make FLIM technology more suitable for fast analysis of high-throughput data, a variety of new algorithms for fluorescence lifetime analysis have emerged in recent years, such as phasor analysis, maximum likelihood estimation, first-order moment, Bayesian analysis, and compressed sensing. Among them, the phasor analysis (PA) method obtains the fluorescence lifetime by converting the fitting in the time domain to the direct calculation in the frequency domain. Compared with traditional least-square fitting method, it is not only simpler and faster, but also more suitable for the case of low photon counts. In addition, in the PA approach to FLIM, the fluorescence decay is directly converted into a phasor diagram by simple mathematics, where the phasor points originating from different pixels in the image are represented by the positions in the phasor plot, and thus the graphical representation obtained by PA method is convenient for data visualization and cluster analysis. Therefore, it has become a simple and powerful analysis method for FLIM, and is increasingly favored by researchers. In this paper, the basic principle of PA method and how we can use it are described in detail. And on this basis, the latest application research progress of the method in cell metabolism state measurement, protein interaction study, cell microenvironment measurement, auxiliary pathological diagnosis, and resolution improvement in super-resolution imaging are introduced and summarized. The advantages of PA method in these FLIM applications are focused on, providing useful reference for the research in related fields. Finally, the phasor analysis method for FLIM data analysis and the development trend of its application are prospected.

Gyro Error Compensation in Optoelectronic Platform Based on a Hybrid ARIMA-Elman Model

As an important angle sensor of the opto-electric platform, gyro output accuracy plays a vital role in the stabilization and track accuracy of the whole system. It is known that the generally used fixed-bandwidth filters, single neural network models, or linear models cannot compensate for gyro error well, and so they cannot meet engineering needs satisfactorily. In this paper, a novel hybrid ARIMA-Elman model is proposed. For the reason that it can fully combine the strong linear approximation capability of the ARIMA model and the superior nonlinear compensation capability of a neural network, the proposed model is suitable for handling gyro error, especially for its non-stationary random component. Then, to solve the problem that the parameters of ARIMA model and the initial weights of the Elman neural network are difficult to determine, a differential algorithm is initially utilized for parameter selection. Compared with other commonly used optimization algorithms (e.g., the traditional least-squares identification method and the genetic algorithm method), the intelligence differential algorithm can overcome the shortcomings of premature convergence and has higher optimization speed and accuracy. In addition, the drift error is obtained based on the technique of lift-wavelet separation and reconstruction, and, in order to weaken the randomness of the data sequence, an ashing operation and Jarque-Bear test have been added to the handle process. In this study, actual gyro data is collected and the experimental results show that the proposed method has higher compensation accuracy and faster network convergence, when compared with other commonly used error-compensation methods. Finally, the hybrid method is used to compensate for gyro error collected in other states. The test results illustrate that the proposed algorithm can effectively improve error compensation accuracy, and has good generalization performance.

A Novel Approach to Array Manifold Calibration Using Single-Direction Information for Accurate Direction-of-Arrival Estimation

A method of array manifold calibration using one steering vector measured in a single direction is proposed. The phase information of the measured steering vector is used to derive a novel calibration matrix that is proposed to compensate for the relative phase distortion (RPD) at each antenna port. We also present a metric function defined as a standard deviation of the RPD to determine the optimum calibration angle, which provides intuition for the cause of the accuracy degradation in the direction-of-arrival estimation. To verify the feasibility, a seven-element circular array with identical microstrip patch antennas is fabricated for calibrating its array manifold using a single steering vector measured in a full anechoic chamber. The calibrated array manifold is then used to estimate the direction of arrival, and its accuracy is compared to the calibrated result obtained from the traditional least-squares method. The results demonstrate that the estimation error can be improved by 54.9° compared to the traditional least-squares method, when the number of measured steering vectors is extremely limited.

Maximum likelihood estimation based regression for multivariate calibration

In this paper, we propose a maximum likelihood estimation based regression (MLER) model for multivariate calibration. The proposed MLER method seeks for the maximum likelihood estimation (MLE) solution of the least-squares problem, and it is much more robust to noise or outliers and accurate than the traditional least-squares method. An efficient iteratively reweighted least squares technique is proposed to solve the MLER model. As a result, our model can obtain accurate spectra–concentrate relations. Experimental results on three real near-infrared (NIR) spectra data sets demonstrate that the proposed MLER model is much more efficacious and effective than state-of-the-art partial least squares (PLS) methods.

Adjustment of non-typical errors-in-variables models

In this contribution, non-typical errors-in-variables (EIV) model is introduced as a more general form of the so-called EIV model which is highly relevant for geodetic data processing. Total least-squares (TLS) algorithms within a typical EIV model cannot deal with the non-typical EIV models since the first order moment/mean of the random design matrix in a non-typical EIV model is not linear. In this paper, we propose a new algorithm besides a standard solution to deal with this model. To achieve this goal, first we review a classic algorithm in order to solve this problem using traditional non-linear least-squares method within a non-linear mixed model. Then by comparison, weighted TLS algorithm within the typical EIV model can be replaced by the proposed approach after some slight modifications which results in an excellent approximate solution. This foundation is important because there is no need for linearization in the TLS algorithms. The proposed way is not sensitive to the approximate initial values of the unknown parameters and it is applicable to curve fitting, surface reconstruction or other non-typical EIV models. Here we employ it to the curve fitting. Also two examples convincingly demonstrate that the standard TLS solution of the non-typical EIV model is not admissible when it is incorrectly considered as a typical EIV model; i.e., the non-linear relationships of the elements of the random design matrix are neglected.

Maximum Likelihood Whitening Pre-filtered Total Least Squares for Resolving Closely Spaced Signals

This paper presents whitening pre-filtered total least squares based on the maximum likelihood technique for root selection to resolve closely spaced signals for linear prediction. A frequency-weighting filter applied to the total least-squares method is commonly used to handle the problem of frequency estimation. This solution provides better performance than the traditional total least-squares technique does when the signal-to-noise ratio is low. However, the performance of total least squares using frequency- weighting filters yields biased effects when the signal-to-noise ratio is high, even worse than the traditional total least-squares method. In view of this, a whitening pre-filtered total least squares based on the maximum likelihood technique for roots selection is introduced. This technique can use the information from the output of the pre-filtered data to eliminate the bias inherent in the frequency-weighting filter method, and most importantly to maintain decent performance levels for a wide range of signal-to-noise ratios.

Pencil beam pattern synthesis of subarrayed planar array

The improved nonlinear least-square method is introduced into the synthesis of subarrayed planar array. This method changes the traditional least-square method's shortness of being sensitive to its initial conditions. The whole antenna aperture is divided into several subarrays and the excitation amplitude of each subarray is optimized. This can reduce the cost and complexity of the antenna array through common use of components or mass production of identical subarrays. Some numerical experiments are provided to show the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:56–65, 2015.