Nonlinear Least-squares Algorithm Research Articles

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

Weld quality prediction of AA 5052-H32 aluminium alloy using neural network approach

In this work, a neural network model is constructed to predict the weld quality of friction stir welded AA 5052-H32 Al alloy plates. The welds quality is evaluated in terms of tensile strength and percentage of elongation. Welding experiments are designed with 31 runs using central composite response surface method. The experimental data is used to develop a multilayered feed forward neural network for training by supervised learning. The network is trained by Levenberg–Marquardt back propagation algorithm for non-linear least Squares. Finally, it is evident that the constructed model predicts the necessary outputs with less than 5% error.

Automatic segmentation of multi-class images with NLS model

In this paper, automatic segmentation of multi-class images problem is considered. The 1D histogram of the multi-class image is approximated using Gaussian functions and the unknown parameters of the Gaussian functions are estimated using Non-linear Least Squares (NLS) optimisation; thereby the problem of segmentation of unknown image class is modelled as an optimisation problem. Further, the parameter estimation accuracy is improved by using the Pearson linear correlation coefficient as a regularisation term of the objective function. The experimental results demonstrate the NLS algorithm ability to estimate the parameters of the Gaussian functions and thereby automatically determine the multi-thresholds for segmentation.

Estimation of cis-eQTL effect sizes using a log of linear model.

The study of expression Quantitative Trait Loci (eQTL) is an important problem in genomics and biomedicine. While detection (testing) of eQTL associations has been widely studied, less work has been devoted to the estimation of eQTL effect size. To reduce false positives, detection methods frequently rely on linear modeling of rank-based normalized or log-transformed gene expression data. Unfortunately, these approaches do not correspond to the simplest model of eQTL action, and thus yield estimates of eQTL association that can be uninterpretable and inaccurate. In this article, we propose a new, log-of-linear model for eQTL action, termed ACME, that captures allelic contributions to cis-acting eQTLs in an additive fashion, yielding effect size estimates that correspond to a biologically coherent model of cis-eQTLs. We describe a non-linear least-squares algorithm to fit the model by maximum likelihood, and obtain corresponding p-values. We perform careful investigation of the model using a combination of simulated data and data from the Genotype Tissue Expression (GTEx) project. Our results reveal little evidence for dominance effects, a parsimonious result that accords with a simple biological model for allele-specific expression and supports use of the ACME model. We show that Type-I error is well-controlled under our approach in a realistic setting, so that rank-based normalizations are unnecessary. Furthermore, we show that such normalizations can be detrimental to power and estimation accuracy under the proposed model. We then show, through effect size analyses of whole-genome cis-eQTLs in the GTEx data, that using standard normalizations instead of ACME noticeably affects the ranking and sign of estimates.

Forward and inverse viscoelastic wave scattering by irregular inclusions for shear wave elastography.

Inversion methods in shear wave elastography use simplifying assumptions to recover the mechanical properties of soft tissues. Consequently, these methods suffer from artifacts when applied to media containing strong stiffness contrasts, and do not provide a map of the viscosity. In this work, the shear wave field recorded inside and around an inclusion was used to estimate the viscoelastic properties of the inclusion and surrounding medium, based on an inverse problem approach assuming local homogeneity of both media. An efficient semi-analytical method was developed to model the scattering of an elastic wave by an irregular inclusion, based on a decomposition of the field by Bessel functions and on a decomposition of the boundaries as Fourier series. This model was validated against finite element modeling. Shear waves were experimentally induced by acoustic radiation force in soft tissue phantoms containing stiff and soft inclusions, and the displacement field was imaged at a high frame rate using plane wave imaging. A nonlinear least-squares algorithm compared the model to the experimental data and adjusted the geometrical and mechanical parameters. The estimated shear storage and loss moduli were in good agreement with reference measurements, as well as the estimated inclusion shape. This approach provides an accurate estimation of geometry and viscoelastic properties for a single inclusion in a homogeneous background in the context of radiation force elastography.

Compressed-sensing wavenumber-scanning interferometry

The Fourier transform (FT), the nonlinear least-squares algorithm (NLSA), and eigenvalue decomposition algorithm (EDA) are used to evaluate the phase field in depth-resolved wavenumber-scanning interferometry (DRWSI). However, because the wavenumber series of the laser's output is usually accompanied by nonlinearity and mode-hop, FT, NLSA, and EDA, which are only suitable for equidistant interference data, often lead to non-negligible phase errors. In this work, a compressed-sensing method for DRWSI (CS-DRWSI) is proposed to resolve this problem. By using the randomly spaced inverse Fourier matrix and solving the underdetermined equation in the wavenumber domain, CS-DRWSI determines the nonuniform sampling and spectral leakage of the interference spectrum. Furthermore, it can evaluate interference data without prior knowledge of the object. The experimental results show that CS-DRWSI improves the depth resolution and suppresses sidelobes. It can replace the FTas a standard algorithm for DRWSI.

Refractive index and surface roughness estimation using passive multispectral and multiangular polarimetric measurements

This paper presents a method to estimate refractive index and surface roughness simultaneously from multispectral and multiangular passive polarimetric measurements. Such a method has ties to passive remote sensing applications. Within the analysis, we use a previously derived expression for the degree of linear polarization, and a nonlinear least-squares algorithm to estimate the parameters of interest (i.e., refractive index and surface roughness) from the measured data. The results obtained from Monte Carlo simulations show that the estimation accuracy improves as the number of spectral channels and detection angles increase. It does so until the estimation accuracy reaches saturation. To take full advantage of the presented method, we also determine the most reasonable number of spectral channels and detection angles for our laboratory measurements using Monte Carlo simulations. Finally, after analyzing the experimental results for dielectric and metallic samples, we validate the effectiveness and advantages of the presented method to estimate refractive index and surface roughness for passive remote sensing.

A Sub-Sampling Approach for Data Acquisition in Gamma Ray Emission Tomography

State of the art data acquisition systems for small animal imaging gamma ray detectors often rely on free running Analog to Digital Converters (ADCs) and high density Field Programmable Gate Arrays (FPGA) devices for digital signal processing. In this work, a sub-sampling acquisition approach, which exploits a priori information regarding the shape of the obtained detector pulses is proposed. Output pulses shape depends on the response of the scintillation crystal, photodetector’s properties and amplifier/shaper operation. Using these known characteristics of the detector pulses prior to digitization, one can model the voltage pulse derived from the shaper (a low-pass filter, last in the front-end electronics chain), in order to reduce the desirable sampling rate of ADCs. Fitting with a small number of measurements, pulse shape estimation is then feasible. In particular, the proposed sub-sampling acquisition approach relies on a bi-exponential modeling of the pulse shape. We show that the properties of the pulse that are relevant for Single Photon Emission Computed Tomography (SPECT) event detection (i.e., position and energy) can be calculated by collecting just a small fraction of the number of samples usually collected in data acquisition systems used so far. Compared to the standard digitization process, the proposed sub-sampling approach allows the use of free running ADCs with sampling rate reduced by a factor of 5. Two small detectors consisting of Cerium doped Gadolinium Aluminum Gallium Garnet (Gd3Al2Ga3O12 : Ce or GAGG:Ce) pixelated arrays (array elements: $2\times 2\times 5~\mathrm {mm}^{3}$ and $1\times 1\times 10~\mathrm {mm}^{3}$ respectively) coupled to a Position Sensitive Photomultiplier Tube (PSPMT) were used for experimental evaluation. The two detectors were used to obtain raw images and energy histograms under 140 keV and 661.7 keV irradiation respectively. The sub-sampling acquisition technique (10 MHz sampling rate) was compared with a standard acquisition method (52 MHz sampling rate), in terms of energy resolution and image signal to noise ratio for both gamma ray energies. The Levenberg-Marquardt (LM) non-linear least-squares algorithm was used, in post processing, in order to fit the acquired data with the proposed model. The results showed that analog pulses prior to digitization are being estimated with high accuracy after fitting with the bi-exponential model.

Isotopic determination of uranium in soil by laser induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) operated under ambient pressure has been evaluated for isotopic analysis of uranium in real-world samples such as soil, with U concentrations in the single digit percentage levels. The study addresses the requirements for spectral decomposition of 235U and 238U atomic emission peaks that are only partially resolved. Although non-linear least-square fitting algorithms are typically able to locate the optimal combination of fitting parameters that best describes the experimental spectrum even when all fitting parameters are treated as free independent variables, the analytical results of such an unconstrained free-parameter approach are ambiguous. In this work, five spectral decomposition algorithms were examined, with different known physical properties (e.g., isotopic splitting, hyperfine structure) of the spectral lines sequentially incorporated into the candidate algorithms as constraints. It was found that incorporation of such spectral-line constraints into the decomposition algorithm is essential for the best isotopic analysis. The isotopic abundance of 235U was determined from a simple two-component Lorentzian fit on the U II 424.437nm spectral profile. For six replicate measurements, each with only fifteen laser shots, on a soil sample with U concentration at 1.1% w/w, the determined 235U isotopic abundance was (64.6±4.8)%, and agreed well with the certified value of 64.4%. Another studied U line – U I 682.691nm possesses hyperfine structure that is comparatively broad and at a significant fraction as the isotopic shift. Thus, 235U isotopic analysis with this U I line was performed with spectral decomposition involving individual hyperfine components. For the soil sample with 1.1% w/w U, the determined 235U isotopic abundance was (60.9±2.0)%, which exhibited a relative bias about 6% from the certified value. The bias was attributed to the spectral resolution of our measurement system – the measured line width for this U I line was larger than its isotopic splitting. Although not the best emission line for isotopic analysis, this U I emission line is sensitive for element analysis with a detection limit of 500ppmU in the soil matrix; the detection limit for the U II 424.437nm line was 2000ppm.

Improvement of depth resolution in depth-resolved wavenumber-scanning interferometry using wavenumber-domain least-squares algorithm: comparison and experiment.

It is important to improve the depth resolution in depth-resolved wavenumber-scanning interferometry (DRWSI) owing to the limited range of wavenumber scanning. In this work, a new nonlinear iterative least-squares algorithm called the wavenumber-domain least-squares algorithm (WLSA) is proposed for evaluating the phase of DRWSI. The simulated and experimental results of the Fourier transform (FT), complex-number least-squares algorithm (CNLSA), eigenvalue-decomposition and least-squares algorithm (EDLSA), and WLSA were compared and analyzed. According to the results, the WLSA is less dependent on the initial values, and the depth resolution δz is approximately changed from δz to δz/6. Thus, the WLSA exhibits a better performance than the FT, CNLSA, and EDLSA.

H, G1, G2 photometric phase function extended to low-accuracy data

We introduce a constrained nonlinear least-squares algorithm to be used in estimating the parameters in the H, G1, G2 phase function. As the algorithm works directly in the magnitude space, it will surpass the possible bias problem that may be present in the existing H,G1,G2 fit procedure when applied to low-accuracy observations with large magnitude variations. With constraints on the photometric phase-curve shape parameters G1 and G2, it guarantees a physically reasonable phase-curve estimate. With a new data set of 93 asteroids, we re-assess the two-parameter version of the H,G1,G2 function. Finally, we introduce a one-parameter version of the phase function that can give a suggestion of the asteroids taxonomic group based only on its phase curve. A statistical model selection procedure is presented that can automatically select between the different versions of the photometric phase functions. An online tool that implements these algorithms is introduced.

Tyre curve estimation in slip-controlled braking

Progress in reducing actuator delays in pneumatic brake systems creates an opportunity for advanced anti-lock braking algorithms to be used on heavy goods vehicles. However, these algorithms require knowledge of variables that are impractical to measure directly. This paper introduces a braking force observer and road surface identification algorithms to support a sliding-mode slip controller for air-braked heavy vehicles. Both the force observer and the slip controller are shown to operate robustly under a variety of conditions in quarter-car simulations. A non-linear least-squares algorithm was found to be capable of performing regressions on all the parameters of the tyre model from the University of Michigan Transportation Research Institute when used ‘in the loop’ with the controller and the observer. A recursive least-squares algorithm that is less computationally expensive than the non-linear algorithm was also investigated but gave only reasonable estimates of the tyre model parameters on high-friction smooth roads.

Imitation of the body/caudal fin undulatory swimming of a spiny dogfish (Squalus acanthias): The kinematic equation

Fishes, with their efficient propulsive systems and wide variety of body shapes, inspire the design of marine robots. To imitate the kinematics of live species for the fish-like robots, some parameters would be extracted by observations from nature. In this article, a summary is presented over the important literature on the kinematics of the body/caudal swimming of fishes. Then, a detailed procedure to extract the kinematic parameters from live species is discussed. In addition, a procedure is presented to account for the length variations of the vertebral column of the live species during their swimming in the modeling of virtual fishes. Different polynomial and exponential amplitude envelope functions associated with single and multiple sinusoidal terms are also adopted to suggest a better kinematic equation for a body/caudal fin swimmer, spiny dogfish shark ( Squalus acanthias). A non-linear least-squares algorithm, Trust-Region, is used to fit surfaces on the experimental data. Results show that in general, the accuracy of the kinematic equation is more affected from the sinusoidal term than the amplitude envelope function. Moreover, evaluations offer the third- and fourth-order polynomial amplitude envelope functions with three sinusoidal terms as appropriate and optimal kinematic equations to model the kinematics of the spiny dogfish shark.

비선형적 최소제곱법을 위한 효율적인 위치추정기법

This paper presents the study of the efficient localization algorithm for non-linear least square estimation. Although non-linear least square(NLS) estimation algorithms are more accurate algorithms than linear least square(LLS) estimation, NLS algorithms have more computation loads because of iterations. This study proposed the efficient algorithm which reduced complexity for small accuracy loss in NLS estimation. Simulation results show the accuracy and complexity of the localization system compared to the proposed algorithm and conventional schemes.

Nonlinear Expectation Maximization Estimator for TDOA Localization

Time-difference-of-arrival (TDOA) techniques are widely used in high-accuracy positioning systems. The weighted nonlinear least squares (NLLS) algorithm can be used in such systems to estimate the target position. If the range measurement errors can be modeled as additive white Gaussian noise (AWGN), the performance of the weighted NLLS algorithm approaches the Cramér-Rao lower bound (CRLB). However, TDOA with weighted NLLS is complex to implement because the covariance matrix of the range measurements is non-diagonal, which requires matrix multiplication and inversion. In this paper, we develop a low-complexity nonlinear expectation maximization localization algorithm. The proposed algorithm is much simpler to implement than the weighted NLLS method since no matrix manipulation is required, while their performances are similar, both approaching the CRLB.

Cardiac T 1 Imaging

T(1) mapping of the heart has evolved into a valuable tool to evaluate myocardial tissue properties, with or without contrast injection, including assessment of myocardial edema and free water content, extracellular volume (expansion), and most recently cardiomyocyte hypertrophy. The magnetic resonance imaging pulse sequence techniques developed for these applications have had to address at least 2 important considerations for cardiac applications: measure magnetization-inversion recoveries during cardiac motion with sufficient temporal resolution for the shortest expected T(1) values, and, second, obtain these measurements within a time during which a patient can comfortably suspend breathing. So-called Look-Locker techniques, and variants thereof, which all sample multiple points of a magnetization recovery after each magnetization preparation, have therefore become a mainstay in this field. The rapid pace of advances and new findings based on cardiac T(1) mapping for assessment of diffuse fibrosis or myocardial edema show that these techniques enrich the capabilities of magnetic resonance imaging for myocardial tissue profiling, which is arguably unmatched by other cardiac imaging modalities.

Joint inversion of seismic refraction and resistivity data using layered models — Applications to groundwater investigation

We developed a method for joint inversion of seismic refraction and resistivity data, using sharp-boundary models with few layers (typically three). We demonstrated the usefulness of the approach via examples from near-surface case studies involving shallow groundwater exploration and geotechnical investigations, although it should also be applicable to other types of layered environments, e.g., sedimentary basins. In our model parameterization, the layer boundaries were common for the resistivity and velocity distributions. Within the layers, only lateral variations in the material parameters (resistivity and velocity) were allowed, and we assumed no correlation between these. The inversion was performed using a nonlinear least-squares algorithm, using lateral smoothing to the layer boundaries and to the materialparameters. Depending on the subsurface conditions, the smoothing can be applied either to the depth of the layer boundaries or to the layer thicknesses. The forward responses and Jacobian for refraction seismics were calculated through ray tracing. The resistivity computations were performed with finite differences and a cell-to-layer transform for the Fréchet derivatives. Our method performed well in synthetic tests, and in the case studies, the layer boundaries were in good agreement with in situ tests and seismic reflection data, although minimum-structure inversion generally has a better data fit due to more freedom to introduce model heterogeneity. We further found that our joint inversion approach can provide more accurate thickness estimates for seismic hidden layers.

Robust Coarse Position Estimation for TDOA Localization

The non-linear least squares (NLLS) algorithm is widely used in localization systems. Its performance approaches the Cramer-Rao lower bound under i.i.d. additive white Gaussian noise. However, when the initial position chosen is not close enough to the actual target position, the NLLS algorithm will very likely diverge. The non-iterative method of moments estimator does not have this divergence problem, but it performs worse than NLLS and requires at least one more anchor to linearize the range measurement equations. In this paper, we develop a coarse position estimation algorithm based on scaling by majorizing a complicated function for time-difference-of-arrival localization, which is robust with regard to the initial position and does not require redundant receivers.

Determination of Young’s modulus, fracture energy and tensile strength of refractories by inverse estimation of a wedge splitting procedure

The wedge splitting test according to Tschegg provides a technique to characterize the fracture behavior of ordinary ceramic refractory materials. By fitting the data from finite element simulation to the results of the wedge splitting test, Young’s modulus and parameters describing the failure behavior under Mode I conditions can be inversely estimated through an adaptive nonlinear least-squares algorithm. The results show Young’s modulus is accurately identified as well as the tensile strength and total specific fracture energy when a trilinear strain softening law is employed. The inversely estimated parameters from three experimental curves of the same material at room temperature are very consistent as well as the values of thermal stress resistance parameter R and characteristic length lch. The method developed enables the identification of the total specific fracture energy, tensile strength and Young’s modulus with numerically robust method in the relatively short time from a single wedge splitting procedure.

Analyses of conformational performance differentiation among functional breeding goals in the Menorca horse breed

<p><strong>Abstract.</strong> The endangered Menorca horse from the Balearic Islands (Spain) is selected for its economically viable traits, such as conformation and dressage performance, while maintaining the maximum possible genetic variability. The aim of this work was to describe the morphology of the Menorca horse and to analyse the conformational variation among the different performance aptitudes of the males (classical dressage, Menorca dressage and leisure) using 47 body measurements and 10 body indices. The data consists of 147 females and 200 males. The Menorca horse can be characterised as an animal of quadrangular format, slim figure with thin and long limbs, with the greatest values for height and length found in the males. The Duncan and principal component analysis with non-linear iterative partial least-squares algorithm discriminates the Menorca dressage group mainly by its differential hind limb angulations. Both the classical and Menorca dressage groups showed well-balanced body proportions for sport performance.</p>