Linear Least-squares Technique Research Articles

Signal and Power Integrity IO Buffer Modeling Under Separate Power and Ground Supply Voltage Variation of the Input and Output Stages

This work presents an improved input–output (IO) buffer model for signal and power integrity simulation, including power/ground supply voltage (PGSV) variations for the buffer’s input and output stages. Both stages are mathematically modeled from a formulation that is derived from nonlinear electrical circuit analysis, an important aspect that grants these models a good level of generality and, simultaneously, high accuracy. The proposed IO buffer model is linear in the parameters and, therefore, extractable through the linear least-squares technique from the signals acquired in an IO buffer characterization setup. Several validation scenarios, supported on two CMOS driver’s transistor technologies, are performed to evaluate the accuracy of the proposed model. In addition, a comparative analysis is provided, confronting the proposed model’s performance against that of the input/output buffer information specification (IBIS) model, evidencing an outstanding modeling improvement provided by the proposed model.

A comparison of domain integral and multi-parameter methods for the strain intensity factor estimation of rigid line inclusion using digital image correlation

A comparative study is carried out between two methods to estimate the strain intensity factor of a rigid line inclusion using the displacement and strain fields from digital image correlation (DIC). The two methods are (i) a proposed hybrid domain integral method and (ii) the linear over-deterministic least-squares technique involving multi-parameter displacement field equations (multi-parameter method). The multi-parameter method uses the displacement data obtained from the DIC experiments to find the unknowns in the multi-parameter equation. The proposed hybrid methodology uses a domain integral method to calculate the strain intensity factor using the full-field displacement and strain data obtained from DIC. The strain intensity factor estimated using the proposed domain integral method, and the multi-parameter method agrees with the analytical estimate. The influence of the size of the annular region and the mesh sensitivity is also reported. The sensitivity to the variance and bias errors in measurement for both the methods is investigated. To investigate the effect of variance error, a Gaussian noise is introduced over the reference and deformed images before post-processing, and its influence on the strain intensity factor estimate is discussed. The effect of random perturbations of displacements and strains on the strain intensity factor estimates is also investigated. The domain integral method is less sensitive to the variance error when compared to the multi-parameter solution approach. Further, the bias errors due to uncorrected lens distortions, over-smoothing of data, and DIC algorithm adopted are introduced into the measurements, and its effect on both the methods is investigated. The multi-parameter method is less sensitive to bias errors when compared to the domain integral method. Therefore, it is recommended that the domain integral method may be used for the experimental determination of strain intensity factor in measurements with variance errors and the multi-parameter method for measurements with bias errors.

Generalized Vertical Components of built-up areas from global Digital Elevation Models by multi-scale linear regression modelling.

The estimation of the vertical components of built-up areas from free Digital Elevation Model (DEM) global data filtered by multi-scale convolutional, morphological and textural transforms are generalized at the spatial resolution of 250 meters using linear least-squares regression techniques. Six test cases were selected: Hong Kong, London, New York, San Francisco, Sao Paulo, and Toronto. Five global DEM and two DEM composites are evaluated in terms of 60 combinations of linear, morphological and textural filtering and different generalization techniques. Four generalized vertical components estimates of built-up areas are introduced: the Average Gross Building Height (AGBH), the Average Net Building Height (ANBH), the Standard Deviation of Gross Building Height (SGBH), and the Standard Deviation of Net Building Height (SNBH). The study shows that the best estimation of the net GVC of built-up areas given by the ANBH and SNBH, always contains a greater error than their corresponding gross GVC estimation given by the AGBH and SGBH, both in terms of mean and standard deviation. Among the sources evaluated in this study, the best DEM source for estimating the GVC of built-up areas with univariate linear regression techniques is a composite of the 1-arcsec Shuttle Radar Topography Mission (SRTM30) and the Advanced Land Observing Satellite (ALOS) World 3D–30 m (AW3D30) using the union operator (CMP_SRTM30-AW3D30_U). A multivariate linear model was developed using 16 satellite features extracted from the CMP_SRTM30-AW3D30_U enriched by other land cover sources, to estimate the gross GVC. A RMSE of 2.40 m and 3.25 m was obtained for the AGBH and the SGBH, respectively. A similar multivariate linear model was developed to estimate the net GVC. A RMSE of 6.63 m and 4.38 m was obtained for the ANBH and the SNBH, respectively. The main limiting factors on the use of the available global DEMs for estimating the GVC of built-up areas are two. First, the horizontal resolution of these sources (circa 30 and 90 meters) corresponds to a sampling size that is larger than the expected average horizontal size of built-up structures as detected from nadir-angle Earth Observation (EO) data, producing more reliable estimates for gross vertical components than for net vertical component of built-up areas. Second, post-production processing targeting Digital Terrain Model specifications may purposely filter out the information on the vertical component of built-up areas that are contained in the global DEMs. Under the limitations of the study presented here, these results show a potential for using global DEM sources in order to derive statistically generalized parameters describing the vertical characteristics of built-up areas, at the scale of 250x250 meters. However, estimates need to be evaluated in terms of the specific requirements of target applications such as spatial population modelling, urban morphology, climate studies and so on.

Synchronization of Auxiliary Mechanisms and Main Electric Drive of the Pipe Cold-Rolling Mill. Complete Solution

This article deals with installations with complex and nonstandard executive instrument movement. Having analyzed the technical implementation and operational features of cold-rolling pipe mills, the research team formulated the problem of synthesizing electric drives of auxiliary mechanisms. It is shown that the conditions for choosing a mechanical converter are associated with the oscillation of the processes of the electric drive system. The finite element method and the gradient descent method are used for structural analysis of solids and electromagnetic calculations. The data of the specific cost of semiconductor converters were analyzed using a linear least-squares regression technique. The advantages of a synchronous reluctance motor of independent excitation for the electric drives of auxiliary mechanisms are given and substantiated. The optimization of the geometrical parameters of the electromechanical converter was carried out according to the maximum developed electromagnetic torque. Modern semiconductor technology in the design of special-purpose electric drives leads to a revision of the principles for determining the optimal number of phases and the structure of the motor power supply. The rationale for the use of multilevel frequency converters is given. Taking into account an in-depth preliminary analysis and an integrated approach, these tasks were successfully completed, which was confirmed experimentally at the implementation of the developed system.

Obtaining Gradients of XCO2 in Atmosphere Using the Constrained Linear Least-Squares Technique and Multi-Wavelength IPDA LiDAR

Integrated-path differential absorption (IPDA) LiDAR is a promising means of measuring the global distributions of the column weighted xCO2 (dry-air mixing ratio of CO2) with adequate accuracy and precision. Most IPDA LiDARs are incapable of discerning the vertical information of CO2 diffusion, which is of great significance for studies on the carbon cycle and climate change. Hence, we developed an inversion method using the constrained linear least-squares technique for a pulsed direct-detection multi-wavelength IPDA LiDAR to obtain sliced xCO2. In the proposed inversion method, the atmosphere is sliced into three different layers, and the xCO2 of those layers is then retrieved using the constrained linear least-squares technique. Assuming complete knowledge of the water vapor content, the accuracy of the retrieved sliced xCO2 could be as high as 99.85% when the signal-to-noise ratio of central wavelength retrievals is higher than 25 (with a log scale). Further experiments demonstrated that different carbon characteristics can be identified by the sign of the carbon gradient of the retrieved xCO2 between the ABL (atmospheric boundary layer) and FT (free troposphere). These results highlight the potential applications of multiple wavelength IPDA LiDAR.

Estimating Code Biases for Criticality Safety Applications with Few Relevant Benchmarks

Criticality safety analyses rely on the availability of relevant benchmark experiments to determine justifiable margins of subcriticality. When a target application lacks neutronically similar benchmark experiments, validation studies must provide justification to the regulator that the impact of modeling and simulation limitations is well understood for the application and often must provide additional subcritical margin to ensure safe operating conditions. This study estimated the computational bias in the critical eigenvalue for several criticality safety applications supported by only a few relevant benchmark experiments. The accuracy of the following three methods for predicting computational biases was evaluated: the Upper Subcritical Limit STATisticS (USLSTATS) trending analysis method; the Whisper nonparametric method; and TSURFER, which is based on the generalized linear least-squares technique. These methods were also applied to estimate computational biases and recommended upper subcriticality limits for several critical experiments with known biases and for several cases from a blind benchmark study. The methods are evaluated based on both the accuracy of their predicted computation bias and upper subcriticality limit estimates, as well as on the consistency of the methods’ estimates, as the model parameters, covariance data libraries, and set of available benchmark data were varied. Data assimilation methods typically have not been used for criticality safety licensing activities, and this study explores a methodology to address concerns regarding the reliability of such methods in criticality safety bias prediction applications.

New weighting factor of weighted CTDI equation for PMMA phantom diameter from 8 to 40 cm: A Monte Carlo study.

The weighted computed tomography dose index (CTDIw ) uses measured CTDI values at the center and periphery of a cylindrical phantom. The CTDIw value is calculated using conventional, Bakalyar's, and Choi's weighting factors. However, these weighting factors were produced from only 16- and 32-cm-diameter cylindrical phantoms. This study aims to devise new weighting factors to provide more accurate average dose in the central cross-sectional plane of cylindrical phantoms over a wide range of object diameters, by using Monte Carlo simulations. Simulations were performed by modeling a Toshiba Aquilion ONE CT scanner, in order to compute the cross-sectional dose profiles of polymethyl methacrylate (PMMA) cylindrical phantoms of each diameter (8-40 cm at 4-cm steps), for various tube voltages and longitudinal beam widths. Two phantom models were simulated, corresponding to the CTDI100 method and the method recommended by American Association of Physicists in Medicine (AAPM) task group 111. The dose-computation PMMA cylinders of 1 mm diameter were located between the phantom surfaces and the centers at intervals of 1 mm, from which cross-sectional dose profiles were calculated. By using linear least-squares fits to the obtained cross-sectional dose profiles data, we determined new weighting factors to estimate more accurate average doses in the PMMA cylindrical phantoms by using the CTDIw equation: CTDIw = Wcenter ・ CTDIcenter + Wperiphery ・ CTDIperiphery . In order to demonstrate the validity of the devised new weighting factors, the percentage difference between average dose and CTDIw value was evaluated for the weighting factors (conventional, Bakalyar's, Choi's, and devised new weighting factors) in each calculated cross-sectional dose profile. With the use of linear least-squares techniques, new weighting factors (Wcenter = 3/8 and Wperiphery = 5/8 where Wcenter and Wperiphery are weighting factors for CTDIcenter and CTDIperiphery ) were determined. The maximum percentage differences between average dose and CTDIw value were 16, -12, -8, and -6% for the conventional, Bakalyar's, Choi's, and devised new weighting factors, respectively. We devised new weighting factors (Wcenter = 3/8 and Wperiphery = 5/8) to provide more accurate average dose estimation in PMMA cylindrical phantoms over a wide range of diameter. The CTDIw equation with devised new weighting factors could estimate average dose in PMMA cylindrical phantoms with a maximum difference of -6%. The results of this study can estimate the average dose in PMMA cylindrical phantoms more accurately than the conventional weighting factors (Wcenter = 1/3 and Wperiphery = 2/3).

Improving the Algorithm of Extracting Regional Total Precipitable Water Vapor Over Land From MODIS Images

Precise estimation of total precipitable water vapor (TPW) with high temporal and spatial resolutions is of great importance in different disciplines. Moderate-Resolution Imaging Spectroradiometer (MODIS) is one of the sensors which have absorption and nonabsorption bands of water vapor. There is a standard algorithm to produce TPW product of MODIS (MOD05/MYD05) which uses the ratios of reflectances in strong, moderate, and weak absorption bands of water vapor to nonabsorption ones (transmission). This paper aims to present a method based on this algorithm to optimize TPW estimation in local scale. To do so, the western part of Iran was chosen as the study region. Terra MODIS images and MOD05 in clear-sky conditions related to the 100 days in four seasons of 2015–2016 were provided as the selected data. To validate and improve the results, TPW measured in six radiosonde stations and interpolated for overpass time of Terra was utilized. Four procedures were performed. In the first procedure, the coefficients of transmissions were extracted using linear least-squares technique, separately. For the second procedure, the coefficients were calculated in terms of the highest atmospheric transmission sensitivity to TPW for each absorption band separately, and in the third procedure, they were calculated simultaneously. In the last procedure, the errors from third one were modeled with a linear relationship between reflectance ratios of absorption bands. Based on the results, in highest accuracy, the coefficient of determination ${{{\text{R}}}}^{2}$ and Root Mean Square Error was 0.878 and 2.702 mm, respectively, which were acceptable comparing those of other researchers.

Direction of arrival tracking for signals with known waveforms based on block least squares techniques

In this paper, we address the problem of tracking DOA of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a nonuniform linear array. Herein, we make use of the fact that the output of each sensor can be described as a linear regression model whose coefficients each contain a pair of DOA and gain information corresponding to one target. These coefficients are determined by solving a linear least squares (LS) problem and then updated recursively based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. Since the coefficients from different sensors have the same amplitude but variable phase information for the same signal, along with simple algebraic manipulations the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space. Computer simulations show that the proposed DOA tracking techniques when applied to a sparse antenna array can provide a better tracking performance than some of the existing methods do.

The effects of ionic strength and organic matter on virus inactivation at low temperatures: general likelihood uncertainty estimation (GLUE) as an alternative to least-squares parameter optimization for the fitting of virus inactivation models

This study examined how the inactivation of bacteriophage MS2 in water was affected by ionic strength (IS) and dissolved organic carbon (DOC) using static batch inactivation experiments at 4 °C conducted over a period of 2 months. Experimental conditions were characteristic of an operational managed aquifer recharge (MAR) scheme in Uppsala, Sweden. Experimental data were fit with constant and time-dependent inactivation models using two methods: (1) traditional linear and nonlinear least-squares techniques; and (2) a Monte-Carlo based parameter estimation technique called generalized likelihood uncertainty estimation (GLUE). The least-squares and GLUE methodologies gave very similar estimates of the model parameters and their uncertainty. This demonstrates that GLUE can be used as a viable alternative to traditional least-squares parameter estimation techniques for fitting of virus inactivation models. Results showed a slight increase in constant inactivation rates following an increase in the DOC concentrations, suggesting that the presence of organic carbon enhanced the inactivation of MS2. The experiment with a high IS and a low DOC was the only experiment which showed that MS2 inactivation may have been time-dependent. However, results from the GLUE methodology indicated that models of constant inactivation were able to describe all of the experiments. This suggested that inactivation time-series longer than 2 months were needed in order to provide concrete conclusions regarding the time-dependency of MS2 inactivation at 4 °C under these experimental conditions.

Global Identification of Mechanical and Electrical Parameters of Asynchronous Motor Driven Joint with a Fast CLOE Method

In many cases of new actuation of compliant controlled or bio-inspired joint driven robot, a global identification of electrical and mechanical coupled dynamics is required. This paper proposes a technique which mixes a closed loop output error method with the inverse dynamic identification model method, which allows for the use of linear least-squares technique to estimate the parameters. A first approach which has been validated on a DC motor achieves a decoupled identification of the electrical and mechanical dynamics but fails to make a simultaneous identification. A major improvement of that method is proposed to carry out the coupled identification of both mechanical and electrical parameters. A validation on an asynchronous motor driven joint shows the effectiveness of the new procedure.

Structural health monitoring of an arch dam from static deformation

This paper presents an investigation of using long-term static deformation measurements for structural health monitoring (SHM) of Fei-Tsui dam, which is located in a very active seismic zone of Taiwan. A modeling technique is developed to characterize the measured static deformation, which is described as a function of the measured physical parameters, where the water level and temperature are the two most important variables affecting dam deformation. The developed modeling method integrates a linear least-squares technique and a nonlinear least-squares process to identify a model by minimizing the residual error between the identified model and the measured static deformation. The proposed modeling technique can also be used for the prediction of the long-term deformation based on the measured water level and temperature for SHM.

Linear trends in cloud top height from passive observations in the oxygen A-band

Abstract. Measurements by the hyperspectral spectrometers GOME, SCIAMACHY and GOME-2 are used to determine the rate of linear change (and trends) in cloud top height (CTH) in the period between June 1996 and May 2012. The retrievals are obtained from Top-Of-Atmosphere (TOA) backscattered solar light in the oxygen A-band using the Semi-Analytical CloUd Retrieval Algorithm SACURA. The physical framework relies on the asymptotic equations of radiative transfer, valid for optically thick clouds. Using linear least-squares techniques, a global trend of −1.78 ± 2.14 m yr−1 in deseasonalized CTH has been found, in the latitude belt within ±60°, with diverging tendencies over land (+0.27 ± 3.2 m yr−1) and ocean (−2.51 ± 2.8 m yr−1). The El Niño–Southern Oscillation (ENSO), strongly coupled to CTH, forces clouds to lower altitudes. The global ENSO-corrected trend in CTH amounts to −0.49 ± 2.22 m yr−1. At a global scale, no explicit regional pattern of statistically significant trends (at 95% confidence level, estimated with bootstrap technique) have been found, which would be representative of typical natural synoptical features. One exception is North Africa, which exhibits the strongest upward trend in CTH sustained by an increasing trend in water vapour.

Covariance and State Estimation of Weakly Observable Systems: Application to Polymerization Processes

Physical models for polymerization may be overly complex considering the available measurements, and they may contain many unobservable and weakly observable modes. Overly complex structures lead to ill-conditioned or singular problems for disturbance variance estimation. Ill conditioning leads to unrealistic data demands for reliable covariance estimates and state estimates. The goal of this paper is to build nonlinear state estimators for weakly observable systems, with focus on polymerization processes. State estimation requires knowledge about the noise statistics affecting the states and the measurements. These noise statistics are usually unknown and need to be estimated from operating data. We introduce a linear time-varying autocovariance least-squares (LTV-ALS) technique to estimate the noise covariances for nonlinear systems using autocorrelations of the data at different time lags. To reduce or eliminate the ill-conditioning problem, we design a reduced-order extended Kalman filter (EKF) to estimate only the strongly observable system states. This reduced filter, which is based on the Schmidt-Kalman filter, is used to perform the estimation of noise covariances by the LTV-ALS technique. Results of the implementation of the proposed method on a large-dimensional ethylene copolymerization example show that better conditioned state and covariance estimation problems can be obtained. We also show that high-quality state estimates can be obtained after the specification of the noise statistics of EKF estimators by ALS.

Experimental Investigation of Emissivity of Steel

In this article, an experimental apparatus for measurements of the emissivity of a metal at different temperatures at \(1.5\, \upmu \text{ m }\) has been developed. Using this apparatus, the emissivity of steel 201, 304, and 321 samples has been measured at different temperatures, and the effects of the temperature, composition, and heating time of steel samples on the emissivity are analyzed according to the measured data. The measured data could be fitted to the same exponential function with the linear least-squares technique, and the fitting accuracy reaches relatively high quality. The measurement uncertainty of this experimental apparatus is analyzed. The analyses show that the measured emissivity is reliable.

Closed-Loop Identification of Multivariable Systems, Using B-Spline Series Expansions for Step Responses

Closed-loop identification is vital in improving underperforming controllers. This paper presents a novel closed-loop identification method for multivariable systems from step responses. The full transfer function matrix of an interactive n × n multivariable process is identified through a sequential step change in the setpoint. The proposed method first approximates the closed-loop step responses, using B-spline series expansions. Based on these expansions, a matrix formulation that represents the closed-loop tests is used to obtain the analytical expressions of open-loop transfer functions. Finally, the reduced low-order models are identified based on the frequency response data by a linear least-squares technique. The proposed identification method is simple and applicable to general multivariable control systems, such as decentralized or centralized control. This method is robust to measurement noise due to the filtering property of the B-splines. Simulation examples have demonstrated the effectiveness of the proposed method for a wide range of multivariable systems.

A new output error method for a decoupled identification of electrical and mechanical dynamic parameters of DC motor-driven robots

Abstract The identification methods based on the inverse dynamic model allow to use the linear least-squares technique to estimate the dynamic parameters (IDIL-LS method) of mechanical and electrical systems. Assuming a good data filtering to calculate derivatives and reference trajectories that excite the system dynamics, this method has been validated through the experimental identification. Recently, an output error (OE) avoids calculating the derivatives of actual data. This is possible by using the same reference trajectory and the same control law for the actual system and the simulated one. The optimal parameters minimize the 2-norm of the error between the actual output y and the simulated one ys. This nonlinear least-squares problem is dramatically simplified using the inverse dynamic model which is linear to the parameters. This method, called DIDIM (Direct and Inverse Dynamic Identification models), has been validated on robot's dynamic parameters identification. In this paper, DIDIM is applied to the decoupled identification of the electrical and mechanical dynamic parameters of DC motor-driven robots using only the reference control voltage of the PWM amplifier and the current reference of the current loop.

Dynamic identification of a 6 dof industrial robot with a closed-loop output error method

AbstractOff-line robot dynamic identification methods are mostly based on the use of the inverse dynamic model, which is linear with respect to the dynamic parameters. This model is sampled while the robot is tracking reference trajectories that excite the system dynamics. This allows using linear least-squares techniques to estimate the parameters. This method requires the joint force/torque and position measurements and the estimate of the joint velocity and acceleration, through the bandpass filtering of the joint position at high sampling rates. Recently, the DIDIM method has been proposed and validated on a 2 degree-of-freedom robot. DIDIM method requires only the joint force/torque measurement. It is a closed-loop output error (CLOE) method based on a closed-loop simulation of the robot using the direct dynamic model, the same structure of the control law, and the same reference trajectory for both the actual and the simulated robot. The optimal parameters minimize the 2-norm of the error between the actual force/torque and the simulated force/torque. A validation experiment on a 6 dof Staubli TX40 robot shows that DIDIM method is very efficient on industrial robots.

A New Closed-Loop Output Error Method for Parameter Identification of Robot Dynamics

Offline robot dynamic identification methods are mostly based on the use of the inverse dynamic model, which is linear with respect to the dynamic parameters. This model is sampled while the robot is tracking reference trajectories that excite the system dynamics. This allows using linear least-squares techniques to estimate the parameters. The efficiency of this method has been proved through the experimental identification of many prototypes and industrial robots. However, this method requires the joint force/torque and position measurements and the estimate of the joint velocity and acceleration, through the bandpass filtering of the joint position at high sampling rates. The proposed new method called DIDIM requires only the joint force/torque measurement, which avoids the calculation of the velocity and acceleration by bandpass filtering of the measured position. It is a closed-loop output error method where the usual joint position output is replaced by the joint force/torque. It is based on a closed-loop simulation of the robot using the direct dynamic model, the same structure of the control law, and the same reference trajectory for both the actual and the simulated robot. The optimal parameters minimize the 2-norm of the error between the actual force/torque and the simulated force/torque. This is a nonlinear least-squares problem which is dramatically simplified using the inverse dynamic model to obtain an analytical expression of the simulated force/torque, linear in the parameters. A validation experiment on a two degree-of-freedom direct drive rigid robot shows that the new method is efficient.

Ignition delay time correlations for a diesel fuel with application to engine combustion modelling

New diesel engine combustion concepts, such as the homogeneous charge compression ignition (HCCI), have encouraged the development of ignition delay correlations allowing the reliable prediction of the chemical auto-ignition time of the fuel, which depends on its oxidation kinetics. These correlations permit one to design and optimize the most adequate control strategies leading to both low emission levels of pollutants and proper engine performance. Although some diesel ignition correlations can be found in the literature, most of them consider the physical delay time and have been obtained only for high temperature values, which are usual at the end of the compression stroke in traditional diesel engines. However, there is still a significant lack of information regarding the complex three-stage oxidation (low-, intermediate-, and high-temperature range) of a diesel fuel under HCCI conditions. Thus the proposal of delay time correlations for the three temperature ranges is the objective of the present work. The correlations have been assumed as Arrhenius-type equations and consider the effect of the main parameters affecting the auto-ignition time, i.e. pressure, temperature, and equivalence fuel/air ratio. The adjustment coefficients have been calculated by using multiple linear regression and least-squares techniques, and a very good fit between modelling-predicted and correlation-predicted delay values has been obtained ( R2 higher than 0.95 in all cases).