Linear Least-squares Research Articles

Instantaneous amplitude and phase signal modeling for harmonic removal in wind turbines

We present a novel approach to harmonic disturbance removal in single-channel wind turbine acceleration data by means of time-variant signal modeling. Harmonics are conceived as a set of quasi-stationary sinusoids whose instantaneous amplitude and phase vary slowly and continuously in a short-time analysis frame. These non-stationarities in the harmonics are modeled by low-degree time polynomials whose coefficients capture the instantaneous dynamics of the corresponding waveforms. The model is linear-in-parameters and is straightforwardly estimated by the linear least-squares algorithm. Estimates from contiguous analysis frames are further combined in the overlap-add fashion in order to yield overall harmonic disturbance waveform and its removal from the data. The algorithm performance analysis, in terms of input parameter sensitivity and comparison against three state-of-the-art methods, has been carried out with synthetic signals. Further model validation has been accomplished through real-world signals and stabilization diagrams, which are a standard tool for determining modal parameters in many time-domain modal identification algorithms. The results show that the proposed method exhibits a robust performance particularly when only the average rotational speed is known, as is often the case for stand-alone sensors which typically carry out data pre-processing for structural health monitoring. Moreover, for real-world analysis scenarios, we show that the proposed method delivers consistent vibration mode parameter estimates, which can straightforwardly be used for structural health monitoring.

A Novel Robust Point Cloud Fitting Algorithm Based on Nonlinear Gauss–Helmert Model

Point cloud fitting plays an important role in various applications of laser scanning technology. Currently, the most dominant algorithms are the linear least-squares (LS) method and the random sample consensus (RANSAC) algorithm, in which the random noises of the point cloud coordinates and the influence of the corresponding stochastic model cannot be fully considered. In this study, the mathematical model of point cloud fitting is uniformly described using the nonlinear Gauss–Helmert (NGH) model, in which the nonlinear relationship between the measurements and parameters, as well as the effects of all random errors, can be considered. In addition, the covariance matrix of point cloud coordinates obtained from the precision of the original measurements is employed to construct the corresponding stochastic model. By further introducing an equivalent weight scheme of robust estimation, a novel point cloud fitting method is proposed based on the robust NGH (RNGH) model. Unlike the previous studies, the RNGH-based algorithm can effectively resist the negative effects of outliers with full consideration of all random errors in various linear and nonlinear fitting problems. To verify the performance of the proposed RNGH, comparative experiments of point cloud fitting are employed in both simulated and real-world scenarios, respectively. The results demonstrate that the proposed point cloud fitting algorithm has significant advantages over LS and RANSAC in terms of accuracy and robustness.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

A new form of LSMR for solving linear systems and least-squares problems

A new form of LSMR for solving linear systems and least-squares problems

A new form of LSMR for solving linear systems and least-squares problems

A new form of LSMR for solving linear systems and least-squares problems

Quantification of bone metabolic activity in the natural course of fractural lesions measured by quantitative SPECT/CT.

While increased uptake at the bone fractural site gradually decreases over time on bone scans, the rate of change has not been quantitatively evaluated. The purpose of this study was to quantify the extent of bone metabolic changes in fractural lesions on bone SPECT/CT. We reviewed bone scans acquired by dedicated SPECT/CT and chose those scans in which quantitative SPECT/CT of the same range was acquired twice or more. We set the region of interest on lesions of bone fracture and degeneration, and measured the maximum standardized uptake value (SUVmax). From the SUVmax of lesions and the interval between scans, a value for 30-day change in SUVmax was calculated as ∆SUVmax30d. The relationship between preSUVmax, SUVmax for the first scan of the comparison, and ∆SUVmax30d was evaluated utilizing a linear least-squares method. Furthermore, we assessed the ability to differentiate between fracture and degeneration using receiver operating characteristics (ROC) analysis and the Mann-Whitney U test. All cases were then categorized into five groups according to preSUVmax. Values of p <0.05 were considered statistically significant. We investigated 175 scans from 60 patients and analyzed scan combinations for 157 fractural lesions and 266 degenerative lesions. The relationship between preSUVmax of fractural lesions and ∆SUVmax30d was approximated as ∆SUVmax30d =-0.15×preSUVmax +1.35 (R 2=0.60, p<0.0001). Area under the curves for all cases, 30≤ preSUVmax, 20≤ preSUVmax <30, 15≤ preSUVmax <20, 10≤ preSUVmax <15, and preSUVmax <10 were 0.73, 0.89, 0.86, 0.80, 0.91, and 0.59, respectively. Median ∆SUVmax30d was significantly lower at fractural lesions than at degenerative lesions (-0.62 vs -0.04; p <0.0001). As for analyses of groups divided by preSUVmax, all median ∆SUVmax30d for fractural lesions were significantly lower than those of degenerative lesions except for the group with preSUVmax <10. The increased uptake at the fractural bone lesion observed in the quantitative bone SPECT/CT gradually decreased at the rate of SUV 0.15 per month, which showed a different trend with degenerative change.

593: PRE-COVID, COVID, AND POST-COVID TRENDS OF RSV AND INFLUENZA ACROSS GEOGRAPHIC REGIONS IN THE USA

Introduction: Admissions to Pediatric Intensive Care Units (PICUs) for respiratory illnesses, particularly RSV and Influenza (INF), have decreased during the COVID-19 pandemic. The differences in trends for RSV and INF admissions to PICUs across different regions in the U.S. are unknown. Changes in these trends before (2014-19), during (2019-20), and towards the end of the pandemic (2021-22), and utilization patterns across regions have not been evaluated. This analysis aimed at addressing these questions. Methods: 874,066 USA PICU cases from the Virtual Pediatric Systems database (myvps.org), from Q1-2014 to Q2-2022, were used to study RSV and INF in patients < 18 years. The geographic regions according to U.S. Census definition included Mid-West (MW), Northeast (NE), South (S), and West (W). RSV and INF were defined by ICD-9 and ICD-10 codes. After removing low-risk patients (PRISM III POD < 0.004) the cohort size was 492,642. Segmented regression analysis (Muggeo 2016) was used to fit the trends in yearly rates for RSV and INF. Least-squares linear fits were applied to data segments before and after breakpoints (change in slope) to determine the correlation coefficients of each segment. Fisher’s Z-transform was used to investigate significant differences between segments before and after their respective breakpoints. Utilization amongst regions was done by ANCOVA analysis, and Bonferroni corrected p-values for the most prevalent procedures in the cohorts. Results: All regions showed an increase in RSV and INF between 2014-19, but decreasing during 2020-21. In 2021-22 all regions showed an increase trend in INF, but RSV increased only in MW and S compared to NE and W. Further analysis using RSV segmented regression revealed: MW, NE, and W breakpoints (positive to negative) in: 2018, 2019, and 2019, respectively. For INF, breakpoints for MW, NE, S, and W were detected in: 2019, 2020, 2019, and 2019, respectively. CPAP use in W was greater than S (p< 0.02). All other procedure comparisons had p-values>0.05. Conclusions: RSV and INF increased in all regions during pre-COVID. RSV and INF decreased in all regions during COVID. INF increased in all the regions towards the end of pandemic. RSV increased in MW and S near the end of the pandemic. Differences in use of CPAP for RSV were found between W and S.

Testing JENDL-5 data for U-235, Pu-239 and U-238 above the resolved resonance region

Recently released JENDL-5 data are extensively tested for U-235, Pu-239 and U-238 above the resolved energy region. For this purpose, a sequence of effective multiplication factors along with some spectral indices for well documented bare and reflected cores of fast systems having a hard spectrum and exhibiting larger sensitivity to data of these actinides, 40 parameters in total, are computed by means of a stochastic technique based upon the Serpent code. This approach is then used along with consistent JENDL-5 covariance data to perform adjustments in conjunction with the Asymptotic Generalized Linear Least-Squares (AGLLS) and Asymptotic Progressing nuclear data Incremental Adjustment (APIA) assimilation methodologies. In the provided example the adjustment largely relies on fission reaction rates per atom for Pu-239 relative to the fission of U-235 measured at core center for Godiva and Jezebel and one effective multiplication factor for an intermediate enrichment uranium system. The latter is sensitive to U-238 data.Despite the good performance of the JENDL-5 library, the illustrative adjustment provides overall improvements of the calculation results in terms of decreased mean χ2 and especially reduced variance of the individual χ2 s. More precisely, the posterior mean χ2 of the 40 parameters is close to one as aimed for. This outcome along with the lowered variance signalize a better consistence of the posterior as compared to the prior results despite the small-size assimilation database.

Signal Source Localization with Long-Term Observations in Distributed Angle-Only Sensors.

Angle-only sensors cannot provide range information of targets and in order to determine accurate position of a signal source, one can connect distributed passive sensors with communication links and implement a fusion algorithm to estimate target position. To measure moving targets with sensors on moving platforms, most of existing algorithms resort to the filtering method. In this paper, we present two fusion algorithms to estimate both the position and velocity of moving target with distributed angle-only sensors in motion. The first algorithm is termed as the gross least square (LS) algorithm, which takes all observations from distributed sensors together to form an estimate of the position and velocity and thus needs a huge communication cost and a huge computation cost. The second algorithm is termed as the linear LS algorithm, which approximates locations of sensors, locations of targets, and angle-only measures for each sensor by linear models and thus does not need each local sensors to transmit raw data of angle-only observations, resulting in a lower communication cost between sensors and then a lower computation cost at the fusion center. Based on the second algorithm, a truncated LS algorithm, which estimates the target velocity through an average operation, is also presented. Numerical results indicate that the gross LS algorithm, without linear approximation operation, often benefits from more observations, whereas the linear LS algorithm and the truncated LS algorithm, both bear lower communication and computation costs, may endure performance loss if the observations are collected in a long period such that the linear approximation model becomes mismatch.

Single-shot attenuation coefficient estimation for ultrasound contrast agents

Ultrasound contrast agents (UCAs) have broadened the scope of ultrasound imaging and therapeutic applications. One of the parameters of interest when measuring the response of UCAs to ultrasound is their frequency-dependent attenuation coefficient. The estimation of this parameter is relevant for sensing and therapeutic applications, as well as for obtaining the viscoelastic properties of the UCA’s shell. The current practice to obtain this coefficient relies on experimental measurements made both in the presence and absence of UCAs in a target medium. Not only is the microbubble-free reference measurement time-consuming, but it may also not always be feasible for in vivo applications due to lack of an appropriate reflector. To overcome these challenges, we present here a novel approach which estimates the UCA’s attenuation spectra directly from pulse-echo measurements made in the underlying UCA medium, without any reference measurement. Furthermore, despite the non-linear frequency dependency of the UCA’s attenuation profile, our approach can still benefit from a fast linear least-squares based estimation scheme, providing attenuation estimates in a single-shot, which is desirable for implementation in real-time systems. We provide an investigative study, testing the estimator’s performance on various simulated realistic attenuation profiles obtained by varying the shell parameters and the UCA’s size distribution. In all cases, the estimated attenuation profiles were in good agreement with the true ones, with a relative error &lt; 10%. Evaluation on experimental in vitro data shows a relative error &lt; 15%, which further highlights the potential of our approach for fast and accurate UCA’s attenuation estimation.

An Exposure Invariant Neural Network for Colour Correction

Colour correction is the process of converting camera dependent RGB values to a camera independent standard colour space such as CIE XYZ. Regression methods &#x2014; linear, polynomial, and root-polynomial least-squares &#x2014; are traditionally used to solve for the colour correction transform. More recently neural net solutions for colour correction have been developed. This paper begins with the observation that the neural net solution &#x2014; while delivering better colour correction accuracy compared to the simple (and widely deployed) 3&#xD7;3 linear correction matrix approach &#x2014; is not exposure invariant. That is to say, the network is tuned to mapping RGBs to XYZs for a fixed exposure level and when this exposure level changes, its performance degrades (and it delivers less accurate colour correction compared to the 3x3 matrix approach which is exposure invariant). We develop two remedies to the exposure variation problem. First, we augment the data we use to train the network to include responses for many different exposures. Concomitantly, the trained network is robust to a changing exposure. Second, we redesign the network so, by construction, it is exposure invariant. Experiments demonstrate that, by adopting either approach, Neural Network colour correction can be made exposure invariant.

Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

Time-dependent diffusivity and kurtosis in phantoms and patients with head and neck cancer.

To assess the reliability of measuring diffusivity, diffusional kurtosis, and cellular-interstitial water exchange time with long diffusion times (100-800 ms) using stimulated-echo DWI. Time-dependent diffusion MRI was tested on two well-established diffusion phantoms and in 5 patients with head and neck cancer. Measurements were conducted using an in-house diffusion-weighted STEAM-EPI pulse sequence with multiple diffusion times at a fixed TE on three scanners. We used the weighted linear least-squares fit method to estimate time-dependent diffusivity, , and diffusional kurtosis, . Additionally, the Kärger model was used to estimate cellular-interstitial water exchange time ( ) from . Diffusivity measured by time-dependent STEAM-EPI measurements and commercial SE-EPI showed comparable results with R2 above 0.98 and overall 5.4± 3.0% deviation across diffusion times. Diffusional kurtosis phantom data showed expected patterns: constant and = 0 for negative controls and slow varying and for samples made of nanoscopic vesicles. Time-dependent diffusion MRI in patients with head and neck cancer found that the Kärger model could be considered valid in 72% ± 23% of the voxels in the metastatic lymph nodes. The median cellular-interstitial water exchange time estimated for lesions was between 58.5 ms and 70.6ms. Based on two well-established diffusion phantoms, we found that time-dependent diffusion MRI measurements can provide stable diffusion and kurtosis values over a wide range of diffusion times and across multiple MRI systems. Moreover, estimation of cellular-interstitial water exchange time can be achieved using the Kärger model for the metastatic lymph nodes in patients with head and neck cancer.

Extraction of photovoltaic generator parameters through combination of an analytical and iterative approach

&lt;span&gt;In the present work, we propose an improved method based on a combination of an analytical and iterative approach to extract the photovoltaic (PV) module parameters using the measured current-voltage characteristics and the simple diode model. First, we calculate the series resistance using a set of analytical formulas for the base values of the three current-voltage curves. Then, the three other parameters are analytically expressed as functions of serial resistance and ideality factor based on the linear least-squares method. Finally, the ideality factor is calculated applying an iterative algorithm to minimize the normalized root mean square error (NRMSE) value. The proposed method was validated with a real experimental set of two PV generators, which showed the best fit to the I-V curve. Moreover, the proposed method needs only the initial value of the ideality factor.&lt;/span&gt;

Online State Estimation for Time-Varying Systems

The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares approach—well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix—the article proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.

A Maximum Power Point Tracking Control Method Based on Rotor Speed PDF Shape for Wind Turbines

Maximum power point tracking (MPPT) is the key to improve the conversion efficiency of wind energy. Concerning the current research on the MPPT control, based on the accurate tracking of rotor speed probability density function (PDF) shape for wind turbines, a novel MPPT algorithm was introduced in detail to improve the power capture and reduce mechanical damage for wind turbines. Considering the influence of wind speed distribution on the wind power generation system performance, this paper expounds a PDF shape control method of a stochastic system based on the Fokker–Planck–Kolmogorov (FPK) equation. Combining the conventional optimal torque (OT) control algorithm with the FPK equation solved by linear least-square (LLS) method, the novel MPPT control law is designed to make the PDF shape of rotor speed track the desired PDF shape as accurately as possible. The simulation verification of the novel MPPT method is carried out in the 1.5 MW wind turbine system. The results reveal that the novel MPPT method can improve the conversion efficiency of wind energy, reduce the frequent fluctuations of system variables, and significantly optimize the performance of wind power generation system.

Universal Graph Filter Design Based on Butterworth, Chebyshev, and Elliptic Functions

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, Chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, Chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the Chebyshev FIR polynomial graph filter design method.

Response time correction of slow-response sensor data by deconvolution of the growth-law equation

Abstract. Accurate high-resolution measurements are essential to improve our understanding of environmental processes. Several chemical sensors relying on membrane separation extraction techniques have slow response times due to a dependence on equilibrium partitioning across the membrane separating the measured medium (i.e., a measuring chamber) and the medium of interest (i.e., a solvent). We present a new technique for deconvolving slow-sensor-response signals using statistical inverse theory; applying a weighted linear least-squares estimator with the growth law as a measurement model. The solution is regularized using model sparsity, assuming changes in the measured quantity occur with a certain time step, which can be selected based on domain-specific knowledge or L-curve analysis. The advantage of this method is that it (1) models error propagation, providing an explicit uncertainty estimate of the response-time-corrected signal; (2) enables evaluation of the solution self consistency; and (3) only requires instrument accuracy, response time, and data as input parameters. Functionality of the technique is demonstrated using simulated, laboratory, and field measurements. In the field experiment, the coefficient of determination (R2) of a slow-response methane sensor in comparison with an alternative fast-response sensor significantly improved from 0.18 to 0.91 after signal deconvolution. This shows how the proposed method can open up a considerably wider set of applications for sensors and methods suffering from slow response times due to a reliance on the efficacy of diffusion processes.

New Results on Classification Modeling of Noisy Tensor Datasets: A Fuzzy Support Tensor Machine Dual Model

In this article, classification problems for a class of tensor datasets with a noisy environment are investigated. To address such issues, a novel fuzzy support tensor machine (FSTM) dual model with robustness is established. First, for each input sample in the noisy tensor dataset, we define three kinds of fuzzy membership functions, such as linear, cosine, and exponential forms. In particular, the reconstruction process from one-dimensional (1-D) vector data to third-order tensor data is also derived in the Appendix. Second, the original optimization model of an FSTM on fuzzy membership is designed by constructing the vector pattern of the traditional support vector machine (SVM) models into a tensor pattern. Next, by introducing the Lagrangian multiplier method and tensor-Tucker decomposition method to the original FSTM model, an FSTM dual model without tensor inner product operation is obtained for the first time. Such a dual model with tensor-Tucker decomposition form can avoid conservativeness caused by the vectorization of tensor data in the traditional SVM model. Furthermore, an FSTM classifier is derived by the designed numerical algorithm, and the classification generalization error bound of the FSTM model with a general form is developed. It is worth noting that a linear least-squares FSTM (LLS-FSTM) equation with tensor-Tucker decomposition is also designed in the Appendix to further reduce the slightly time-consuming problem of the solving the dual optimization model FSTM. Finally, two numerical examples are presented to verify the feasibility and validity of the derived FSTM classifier.

Regression Bias in Using Solar Wind Measurements

Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.