Nonlinear Least-squares Algorithm Research Articles

A simple-to-use nomogram for reference evapotranspiration assessment using multivariate models: Study on outdoor and greenhouse environments

Experimental methods of reference evapotranspiration (ET 0 ) calculation require extensive environmental data, not readily attainable everywhere. Therefore, two multivariate models using Levenberg–Marquardt nonlinear least-squares algorithm were developed in this research to estimate daily ET 0 by focusing on fewer meteorological variable inputs. Different meteorological parameters were measured for two consecutive years in outdoor and greenhouse environments. The ET 0 models were developed for the aforementioned environments in terms of three major parameters, namely air temperature, relative humidity and pan evaporation. To construct the ET 0 models, three steps were carried out, (i) outdoor wind speed was estimated in terms of the major parameters with appropriate accuracy (R 2 = 0 . 42 , AR 2 = 0 . 4 and RMSE = 0.176 m/s), (ii) net radiation was estimated in terms of the major parameters and estimated wind speed with high accuracy (their R 2 and AR 2 > 0.47 and RMSE < 2.55 MJ/(m 2 -day)), and (iii) ET 0 was accurately estimated in terms of the major parameters, estimated wind speed and net radiation. Our ET 0 models (R. & M. models) were compared with nine common methods for both conditions according to eight statistical indices. The results indicated that in the outdoor condition, FPM and R. & M. were the best models, respectively, while Makkink indicated the poorest estimations. In the greenhouse condition, the R. & M. model was the best, FPM was the third-best and Linacre was the worst method for ET 0 estimation. However, R. & M. models were significantly appropriate for ET 0 assessment, they were multivariate models, so the nomography method was used as a user-friendly method to illustrate the estimations. The difference between the model outputs and nomogram was negligible, indicating that the nomogram was suitable for ET 0 determination and can be used in the weather stations. • Multivariate ET 0 models were developed by focusing on fewer meteorological parameters. • LM algorithm successfully updated the ET 0 model coefficients. • Wind speed and net radiation were modeled as mediator variables for ET 0 modeling. • The R. & M. ET 0 models presented the most accuracy among different reported methods. • ET 0 nomograph provided for outdoor and greenhouse conditions showed good estimation.

Kinetic model for molecular beam epitaxy growth of InAsSbBi alloys

The growth of Bi-containing III-V alloys requires careful control over temperature and group-V fluxes due to the low equilibrium solubility of Bi and its tendency to surface segregate into Bi-rich droplet features. A model for molecular beam epitaxy growth based on the kinetics of atomic desorption, incorporation, surface accumulation, and droplet formation is applied to the bismide alloy InAsSbBi grown on GaSb substrates. A steady-state solution is derived for the Bi, Sb, and As mole fractions and surface layer coverages based on the Bi, Sb, and As fluxes. A nonlinear least-squares algorithm is used to fit the growth model parameters to experimentally measured Bi mole fractions in bulk and quantum well InAsSbBi samples grown at 400 °C and 420 °C. The Bi mole fraction ranges from 0.12% to 1.86% among 17 samples examined. The results indicate that as the growth temperature increases, the rate of Bi incorporation decreases and the rate of Bi self-desorption increases. A strong interaction is observed between Bi and As that plays a role in the desorption of excess Bi from the growth surface, thus reducing the likelihood of Bi-rich droplet formation when an excess As flux is present. Significantly, the model predicts that the incorporation of Bi is limited to mole fractions of 1.43% at 400 °C and 0.30% at 420 °C in lattice-matched bulk InAsSbBi grown on GaSb substrates.

A Regularized Affine-Scaling Trust-Region Method for Parametric Imaging of Dynamic PET Data

Parametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. Classical approaches to parametric imaging rely on linearized schemes that, on the one hand, are computationally effective but, on the other hand, provide information just on a very limited number of parameters (typically two). Possible nonlinearized approaches require the pixelwise numerical solution of compartmental nonlinear ill-posed inverse problems and therefore typically imply a notable computational burden. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling trust-region method. The main advantages of this approach are both that it is a regularization method (and therefore it reduces the numerical instabilities in the reconstructed images) and that it is significantly faster than other algorithms in the optimization market (and therefore it may be utilized for clinical applications). The validation of this approach is realized in a simulation framework for brain imaging and also in the case of an experimental set of nuclear medicine data acquired from a murine model. Comparison of performances is made with respect to a regularized Gauss--Newton scheme and a standard nonlinear bound-constrained least-squares algorithm.

Free-water DTI estimates from single b-value data might seem plausible but must be interpreted with care.

Free-water elimination DTI (FWE-DTI) has been used widely to distinguish increases of free-water partial-volume effects from tissue's diffusion in healthy aging and degenerative diseases. Because the FWE-DTI fitting is only well-posed for multishell acquisitions, a regularized gradient descent (RGD) method was proposed to enable application to single-shell data, more common in the clinic. However, the validity of the RGD method has been poorly assessed. This study aims to quantify the specificity of FWE-DTI procedures on single-shell and multishell data. Different FWE-DTI fitting procedures were tested on an open-source in vivo diffusion data set and single-shell and multishell synthetic signals, including the RGD and standard nonlinear least-squares methods. Single-voxel simulations were carried out to compare initialization approaches. A multivoxel phantom simulation was performed to evaluate the effect of spatial regularization when comparing between methods. To test the algorithms' specificity, phantoms with two different types of lesions were simulated: with altered mean diffusivity or with modified free water. Plausible parameter maps were obtained with RGD from single-shell in vivo data. The plausibility of these maps was shown to be determined by the initialization. Tests with simulated lesions inserted into the in vivo data revealed that the RGD approach cannot distinguish free water from tissue mean-diffusivity alterations, contrarily to the nonlinear least-squares algorithm. The RGD FWE-DTI method has limited specificity; thus, its results from single-shell data should be carefully interpreted. When possible, multishell acquisitions and the nonlinear least-squares approach should be preferred instead.

Heavy oil hydrocracking kinetics with nano-nickel dispersed in PEG300 as slurry phase catalyst using batch reactor

The kinetics of slurry phase heavy oil hydrocracking with nickel nanoparticles dispersed in PEG300 as the slurry phase catalyst was investigated. Colloidal metal nanoparticles were synthesized using a chemical reduction method. Catalytic evaluations were performed in a batch reactor with 7.0 MPa H2 and varying temperatures (310–370 °C) and reaction times (4–72 h). A five-lump kinetic model was used to obtain kinetic parameters using the R software with the Levenberg-Marquardt nonlinear least-squares algorithm. The order of the residue hydrocracking reaction rate equation was 2.5. The activation energies were determined, and the calculated product compositions were in agreement with the experimental values (<5%). The residue exhibited high selectivity towards naphtha. High residue conversion was accomplished, even at low reaction times.

Artificial neural network for multi-echo gradient echo-based myelin water fraction estimation.

To demonstrate robust myelin water fraction (MWF) mapping using an artificial neural network (ANN) with multi-echo gradient-echo (GRE) signal. Multi-echo gradient-echo signals simulated with a three-pool exponential model were used to generate the training data set for the ANN, which was designed to yield the MWF. We investigated the performance of our proposed ANN for various conditions using both numerical simulations and in vivo data. Simulations were conducted with various SNRs to investigate the performance of the ANN. In vivo data with high spatial resolutions were applied in the analyses, and results were compared with MWFs derived by the nonlinear least-squares algorithm using a complex three-pool exponential model. The network results for the simulations show high accuracies against noise compared with nonlinear least-squares MWFs: RMS-error value of 5.46 for the nonlinear least-squares MWF and 3.56 for the ANN MWF at an SNR of 150 (relative gain=34.80%). These effects were also found in the in vivo data, with reduced SDs in the region-of-interest analyses. These effects of the ANN demonstrate the feasibility of acquiring high-resolution myelin water images. The simulation results and in vivo data suggest that the ANN facilitates more robust MWF mapping in multi-echo gradient-echo sequences compared with the conventional nonlinear least-squares method.

Identifying the Parameters of Cole Impedance Model Using Magnitude Only and Complex Impedance Measurements: A Metaheuristic Optimization Approach

Due to the good correlation between the physiological and pathological conditions of fruits and vegetables and their equivalent Cole impedance model parameters, an accurate and reliable technique for their identification is sought by many researchers since the introduction of the model in early 1940s. The nonlinear least squares (NLS) and its variants are examples of the conventional optimization techniques that are commonly used in literature to tackle this problem based on complex-valued impedance measurement data. However, as happens in most conventional techniques, the NLS and its variants are subject to falling local optimal solutions and prone to getting distracted by outliers. This motivated the authors to use six meta-heuristic optimization techniques to estimate the Cole impedance models’ parameters on the basis of either complex impedance or magnitude-only impedance experimental measurements. Most of the meta-heuristic optimization algorithms under investigation are entirely new to this application. These algorithms include the: salp optimization algorithm (SSA), moth-flame optimizer (MFO), whale optimization algorithm (WOA), grey wolf optimizer (GWO), cuckoo search optimizer (CS) and flower pollination algorithm (FPA). The comparison with the NLS algorithm and most of the bio-inspired algorithms under investigation show greater consistency and accuracy with regard to the estimated parameters. A box plot statistical analysis is carried out to prove the effectiveness of the investigated bio-inspired algorithms.

Optimal design of neural modulation strategy of vestibular prosthesis

Objective:To reveal the response characteristics of semicircular canal neurons（SCN） in the nonlinear perceptual interval, and to establish and screen out the precise SCN information coding model and function expression, which lays a foundation for the optimization and improvement of neuromodulation strategy of multichannel vestibular prosthesis. Method:The perceptual electrophysiological information data of the SCNs during the rotational stimulation was recorded in the nonlinear perceptual interval. The nonlinear least-squares algorithm was used to fit the electrophysiological information data to establish the linear-nonlinear models. The Akaike information criterion was used to calculate the goodness of fit of each model to determine the optimal expression function. Result:In the frequency experiment, the accurate information coding model of more than 85% of SCNs is a quadratic polynomial, and the frequency has no significant effect on the linear-nonlinear selection of the SCNs information coding model（P>0.05）. In the amplitude experiment, the accurate information coding model of more than 83.33% of SCNs is quadratic polynomial when the maximum angular velocity is>80 deg/s, and the amplitude has a significant effect on the linear-nonlinear selection of the SCNs information coding model（P=0.038）. Conclusion:The information coding models of SCN population in the nonlinear perceptual interval have two expressions, linear and nonlinear function, which is closely related to angular velocity. The quadratic polynomial function is more accurate and more advantageous and it can be used to design the precise neuromodulation strategy of multichannel vestibular prosthesis.

A novel model-based internal state observer of a fuel cell system for electric vehicles using improved Kalman filter approach

Poor air supply system management usually leads to various degrees of oxygen starvation, which affect the durability and reliability of the proton exchange membrane fuel cell (PEMFC). Real-time internal states monitoring of the cathode side is imperative for feedback control to improve the performance of the air supply system and net power. In this paper, a nonlinear internal state observer that estimates the mass of oxygen and nitrogen inside the cathode of a vehicular PEMFC system is proposed. A lumped parameter dynamic system model for the mass transport process on the cathode side is established and parameterized using a nonlinear least-squares algorithm with a working dataset. The model-based nonlinear observer is designed based on an adaptive cubature Kalman filter (ACKF) algorithm. The adaptive adjustment is implemented to match the covariances of process noise and measurement noise in real-time. Furthermore, the singular value decomposition (SVD) is employed to replace the Cholesky decomposition of the covariance of state variables to improve the convergent stability of the iterative calculation process. The performance of the proposed SVD-ACKF observer is validated and compared with the unscented Kalman filter (UKF) observer and SVD based cubature Kalman filter (SVD-CKF) observer with no adaptive process. The results show that the SVD-ACKF observer demonstrates the best convergence and accuracy, even though various uncertainties in the initial values of the internal states and system parameters, and upon different power requirements.

Geoacoustic inversion using ray-based blind deconvolution of shipping sources.

The ray-based blind deconvolution algorithm can provide an estimate of the channel impulse responses (CIRs) between a shipping source of opportunity and the elements of a receiving array by estimating the unknown phase of this random source through wideband beamforming along a well-resolved ray path. However, due to the shallow effective depth (typically <10 m) and low frequency content (typically less than a few kHz) associated with shipping sources, the interfering direct and surface arriving pair and subsequent bottom and surface-bottom arrival pair cannot always be resolved in the CIR arrival-time structure. Nevertheless, this study demonstrates that the bottom reflection loss can be inferred from the ratio of the magnitude spectra of these two arrival pairs if a frequency-dependent correction (which can be purely data based) is applied to correct for the dipole source effect. The feasibility of the proposed approach is demonstrated to invert for the geoacoustic parameters of a soft-layer covering the ocean floor using a nonlinear least-square algorithm.

A Second-Order Method for Fitting the Canonical Polyadic Decomposition With Non-Least-Squares Cost

The canonical polyadic decomposition (CPD) can be used to extract meaningful components from a tensor. Most existing optimization methods for fitting the CPD use as cost function the least-squares distance between the tensor and its CPD. While the minimum of this cost function coincides with the maximum likelihood estimator for data with additive i.i.d. Gaussian distributed noise, for other noise distributions, better-suited cost functions exist. For such cost functions, first-order, gradient-based optimization methods have been proposed. However, (approximate) second-order methods, which additionally use information from the Hessian of the cost function to achieve faster convergence, are still largely unexplored. In this paper, we generalize the Gauss–Newton nonlinear least-squares algorithm to twice differentiable entry-wise cost functions. The low-rank structure of the problem is exploited to keep the computational cost low. As a special case, $\beta$ -divergence cost functions are examined. We show that quadratic convergence can be obtained close to the solution with a reasonable extra cost in memory and computation time, making the proposed method particularly useful when high accuracy of the decomposition is desired.

Alternating Group Lasso for Block-Term Tensor Decomposition and Application to ECG Source Separation

In some applications, blind source separation can be performed by computing an approximate block-term tensor decomposition (BTD), under much milder constraints than matrix-based techniques. However, choosing the BTD model structure ( i.e. , the number of blocks and their ranks) is a difficult problem, and the standard least-squares formulation can be ill-posed. This paper proposes an alternating group lasso algorithm to compute approximate low-rank BTDs. It solves, in a provably convergent manner, a well-posed mixed-norm regularized tensor approximation problem that allows estimating the model parameters and its structure jointly. A variant is also put forward for dealing with linearly constrained blocks, motivated by the problem of blind separation of sums of complex exponentials, which can be cast as a low-rank Hankel-structured block-term tensor approximation problem. An experimental comparison with a standard nonlinear least-squares algorithm on synthetic tensor data indicates that the proposed algorithm is much more robust with respect to initialization. We also apply the constrained variant to the extraction of atrial activity from semi-synthetic and real-world electrocardiogram recordings during atrial fibrillation episodes. Our results show its ability to consistently select an adequate structure and to extract multiple signals which can be physiologically interpreted as atrial fibrillation patterns.

Sea-Ice Concentration Derived From GNSS Reflection Measurements in Fram Strait

Reflection power derived from the global navigation satellite system (GNSS) observations and its sensitivity to sea-ice concentration are investigated in this article. A corresponding experiment has been conducted during the Fram Strait cruise of the Norwegian research vessel Lance in summer 2016. The dedicated setup with a GNSS Occultation Reflectometry Scatterometry (GORS) receiver and dual-polarization (left- and right-handed) antenna links recorded 1922 h of reflection events during the 20-day cruise of the ship. The antenna setup, mounted 25.0 m above the waterline, serves to acquire sea surface reflections at grazing angles below 30°. Within a 5-min coherent integration period, direct and reflected signal contributions can be separated. Except for the highest sea states, with roll angle changes of 20° peak to peak, the separation allows to retrieve the reflection power and quantifies it in cross-, co-, and cross-to-co-polar ratios. The sea-ice concentration is inverted from power ratios using a non-linear least-squares algorithm. Additional data on sea-ice concentration gathered by a watchman on the ship are used for validation. The inversion results have a 20% resolution in concentration and 3-h resolution in time. The validation shows that the cross- and cross-to-co-polar data are sensitive to the sea-ice concentration. The respective Pearson correlation of 0.75 and 0.67 further suggests studies to foster the application of the GNSS data for sea-ice reflectometry.

KF‐based estimation of diode turn‐off power loss using datasheet information

In this Letter, an effective method for estimation of turn-off power losses of power diodes using datasheet information is proposed. An effective regression method with non-linear least-squares algorithm is used to obtain approximate representations of the reverse-recovery charge and softness factor of the diode using datasheet information. Kalman Filter (KF) algorithm is then used to accurately acquire the value of diode forward current at the turn-off instant. Finally, the obtained information is used to estimate the turn-off power losses with simple calculations, based on approximated reverse-recovery equations. Despite the simplicity of the proposed technique, the results demonstrate that the estimation error does not exceed 4% in the worst case.

A Fast UHF RFID Localization Method Using Unwrapped Phase-Position Model

A novel ultrahigh-frequency (UHF) radio frequency identification (RFID) localization method is proposed in this paper, by which the location of a static passive tag can be easily obtained using a mobile RFID antenna. An unwrapped phase-position model with three parameters is built, and the location of the tag can be pinpointed through an ordinary nonlinear least-squares algorithm. The main advantage of this method is that it is cheap in computation cost compared with the existing grid-based methods. The experimental tests confirm that the proposed method can localize the RFID tags with a competitive computational efficiency and accuracy performance, i.e., millisecond-level computing time and centimeter-level location accuracy. The proposed UHF RFID localization method is well suited to the pervasive location-aware applications, searching RFID-tagged item in the intelligent warehouse by the mobile robot with an onboard RFID system, for example.

Quantitative Analysis of Main Components of Natural Gas Based on Raman Spectroscopy

Abstract Natural gas is composed of methane, ethane, propane, carbon dioxide, nitrogen, hydrogen, carbon monoxide and unknown alkane components of C4 or more (denoted as C4+) after desulfurization and dehydration treatment. The concentrations of the first seven components account for more than 90% of natural gas. When analyzing the natural gas composition using Raman spectral analysis methods, a small amount of unknown alkane components C4+ will have a negative impact on the analytical precision. In this work, a novel method that consists of an automatic decomposition algorithm of Raman spectra and a model for quantitative analysis was developed for the analysis of components of natural gas. The Raman spectrum of a natural gas sample could be decomposed into the sum of the Raman spectra of pure constituents and several Lorentz peaks by a nonlinear least-square optimization algorithm based on a linear additivity of Raman spectra. The concentration of the unknown alkane component C4+ was determined according to the area of the C-H deformation vibration peak which was common for most alkane molecules. Some training samples were used to establish the model between Raman characteristic peak areas and corresponding concentrations for each component. Compared with the existing Raman analysis methods, the new method solved the problem of analyzing natural gas containing unknown alkane components with good stability and accuracy. The experiments showed that the maximum absolute errors of this algorithm for methane, ethane, propane, carbon dioxide, nitrogen, hydrogen, and carbon monoxide respectively reached 0.57%, 0.37%, 0.21%, 0.07%, 0.18%, 0.04%, 0.13%, and the correlation coefficient to gas chromatographic results also reached 0.997, 0.986, 0.991, 0.998, 0.993, 1.000, 0.995, 0.982, respectively.

Intranasal Filtration of Inhaled Aerosol in Human Subjects as a Function of Nasal Pressure Drop.

Intersubject variability in nasal deposition of inhaled aerosol is significant because of the differences in nasal anatomy and breathing rate. The notable limitation of the majority of previously developed predictive correlations is including a limited number of subjects. A few recent studies have considered a wide age range of subjects, but the resulting correlations require the knowledge of the dimensions of the nasal airways and the properties of inhaled gas. In this study empirical correlations are proposed to predict aerosol deposition in nasal airways of subjects of different age as a function of intranasal pressure drop and the particle aerodynamic diameter. The experimental nasal deposition and pressure drop data in anatomically correct nasal replicas of 5 adults, 13 children aged 4-14 years, and 11 infants aged 3-18 months were reanalyzed. The range of aerodynamic diameter was 0.5-5.3 μm and physiological breathing at different activity levels was considered. Correlations between nasal deposition and a deposition parameter including the aerodynamic size of inhaled aerosol and nasal pressure drop were developed with nonlinear least-square algorithms. The general coefficient of determination r2 was used to evaluate the fitting accuracy for each correlation. New correlations were developed to predict the intranasal deposition of particles as a function of intranasal pressure drop and particle size for pediatric and adult subjects. The intranasal deposition fraction in adults and children can be calculated using the same correlation, whereas the intranasal deposition in infants followed a different trend line because of higher intranasal pressure drop in infants. This study was the first offering correlations to predict intranasal deposition in multiple age groups using only the aerodynamic size of inhaled aerosol and nasal pressure drop. These correlations include the effects of intersubject variability in nasal deposition within each age group and among different age groups.

Mechanical characterization of arteries affected by fetal growth restriction in guinea pigs (Cavia porcellus)

Fetal growth restriction (FGR) is a perinatal condition associated with a low birth weight that results mainly from maternal and placental constrains. Newborns affected by this condition are more likely to develop in the long term cardiovascular diseases whose origins would be in an altered vascular structure and function defined during fetal development. Thus, this study presents the modeling and numerical simulation of systemic vessels from guinea pig fetuses affected by FGR. We aimed to characterize the biomechanical properties of the arterial wall of FGR-derived the aorta, carotid, and femoral arteries by performing ring tensile and ring opening tests and, based on these data, to simulate the biomechanical behavior of FGR vessels under physiological conditions. The material parameters were first obtained from the experimental data of the ring tensile test. Then, the residual stresses were determined from the ring opening test and taken as initial stresses in the simulation of the ring tensile test. These two coupled steps are iteratively considered in a nonlinear least-squares algorithm to obtain the final material parameters. Then, the stress distribution changes along the arterial wall under physiological pressure were quantified using the adjusted material parameters. Overall, the obtained results provide a realistic approximation of the residual stresses and the changes in the mechanical behavior under physiological conditions.

Observer-based cyber attack detection and isolation in smart grids

In this paper, we investigate the cyber security problem for large scale smart grid systems under false data injection attack. An observer-based algorithm is proposed to detect and isolate the cyber attack by using real-time synchrophasor measurements. Combining the smart grid system with graph theory, the system is divided into several different coupled areas via sparsity of the connection topology. According to the partition, the system is decomposed equivalently into several areas. Then, the output of the smart grid system can be gotten through wide area measurement system based on PMUs, and the asymmetric weighted Laplacian can be obtained by running a nonlinear least-square estimation algorithm. By designing a modified observer, the residual is computed, and the adaptive residual threshold, used to detect and isolate the attack in the areas of the system, is also shown with considering the system model uncertainties. Then, an iterative algorithm detecting and isolating the cyber attack is proposed based on the calculated residual threshold. Finally, some simulations are provided to illustrate the effectiveness of the proposed algorithm.

Improved liver R2* mapping by pixel-wise curve fitting with adaptive neighborhood regularization.

To improve liver R2* mapping by incorporating adaptive neighborhood regularization into pixel-wise curve fitting. Magnetic resonance imaging R2* mapping remains challenging because of the serial images with low signal-to-noise ratio. In this study, we proposed to exploit the neighboring pixels as regularization terms and adaptively determine the regularization parameters according to the interpixel signal similarity. The proposed algorithm, called the pixel-wise curve fitting with adaptive neighborhood regularization (PCANR), was compared with the conventional nonlinear least squares (NLS) and nonlocal means filter-based NLS algorithms on simulated, phantom, and in vivo data. Visually, the PCANR algorithm generates R2* maps with significantly reduced noise and well-preserved tiny structures. Quantitatively, the PCANR algorithm produces R2* maps with lower root mean square errors at varying R2* values and signal-to-noise-ratio levels compared with the NLS and nonlocal means filter-based NLS algorithms. For the high R2* values under low signal-to-noise-ratio levels, the PCANR algorithm outperforms the NLS and nonlocal means filter-based NLS algorithms in the accuracy and precision, in terms of mean and standard deviation of R2* measurements in selected region of interests, respectively. The PCANR algorithm can reduce the effect of noise on liver R2* mapping, and the improved measurement precision will benefit the assessment of hepatic iron in clinical practice. Magn Reson Med 80:792-801, 2018. © 2018 International Society for Magnetic Resonance in Medicine.