Least-squares Procedure Research Articles

Experimental Investigation of the Hydrodynamic Coefficients of a Remotely Operated Vehicle Using a Planar Motion Mechanism

The determination of hydrodynamic coefficients of full scale underwater vehicles using system identification (SI) is an extremely powerful technique. The procedure is based on experimental runs and on the analysis of on-board sensors and thrusters signals. The technique is cost effective and it has high repeatability; however, for open-frame underwater vehicles, it lacks accuracy due to the sensors’ noise and the poor modeling of thruster-hull and thruster-thruster interaction effects. In this work, forced oscillation tests were undertaken with a full scale open-frame underwater vehicle. These conducted tests are unique in the sense that there are not many examples in the literature taking advantage of a PMM installation for testing a prototype and; consequently, allowing the comparison between the experimental results and the ones estimated by parameter identification. The Morison’s equation inertia and drag coefficients were estimated with two parameter identification methods, that is, the weighted and the ordinary least-squares procedures. It was verified that the in-line force estimated from Morison’s equation agrees well with the measured one except in the region around the motion inversion points. On the other hand, the error analysis showed that the ordinary least-squares provided better accuracy and, therefore, was used to evaluate the ratio between inertia and drag forces for a range of Keulegan–Carpenter and Reynolds numbers. It was concluded that, although both experimental and estimation techniques proved to be powerful tools for evaluation of an open-frame underwater vehicle’s hydrodynamic coefficients, the research provided a rich amount of reference data for comparison with reduced models as well as for dynamic motion simulation of ROVs.

Application of component-wise rank method to bivariate bioequivalence case

AbstractOne of the most common analyses in pharmaceutical research is bioequivalence test of two drugs. The FDA has endorsed the usage of Schuirmann's two one-sided hypotheses for the analyses in such studies. Generally, however, several measures on the drugs are taken simultaneously such that the data are multivariate. Nandakumar and McKean generalized Schuirmann's procedure to this multivariate setting. For bivariate data, the results can be summarized in a graphical display. These procedures are least-squares-type procedures and hence, are quite sensitive to mild outliers. To counter this sensitivity, Nandakumar and McKean also developed a simple highly efficient and robust analogue to their multivariate least-squares procedure. The robust results can also be displayed graphically, overlaid with the least-squares graphical results. In this paper, a SAS algorithm is presented, which implements these least-squares and robust multivariate tests for bioequivalence, including their graphical summaries.

On the evolution of concepts of the least-squares method based on the principle of maximum fisher information

This paper considers the evolution of the least-squares method based on the substitution of the principle of maximum Fisher information for the Gaussian principle of maximum weight and gives working formulae for practical application of the least-squares procedures to maximize Fisher information.

Convergence of an efficient local least-squares fitting method for bases with compact support

The least-squares projection procedure appears frequently in mathematics, science, and engineering. It possesses the well-known property that a least-squares approximation (formed via orthogonal projection) to a given data set provides an optimal fit in the chosen norm. The orthogonal projection of the data onto a finite basis is typically approached by the inversion of a Gram matrix involving the inner products of the basis functions. Even if the basis functions have compact support, so that the Gram matrix is sparse, its inverse will be dense. Thus computing the orthogonal projection is expensive.An efficient local least-squares algorithm for non-orthogonal projection onto smooth piecewise-polynomial basis functions is analyzed. The algorithm runs in optimal time and delivers the same order of accuracy as the standard orthogonal projection. Numerical results indicate that in many computational situations, the new algorithm offers an effective alternative to global least-squares approximation.

Soil water dynamics at a midlatitude test site: Field measurements and box modeling approaches

► Simple box models can describe soil water dynamics at midlatitudes. ► The only meteorological forcing used is daily rainfall. ► Three models are validated both in “in-sample” and in forecast mode. ► Best model: leakage and evapotranspiration are nonlinear functions of soil water. We test the ability of three box models ( Milly, 1993 , Kim et al., 1996 , Laio et al., 2001b ) to describe soil moisture dynamics in a regularly monitored experimental site in northwestern Italy. The models include increasingly complex representations of leakage and evapotranspiration processes. We force the models with the local rainfall, and we determine model parameters with a least-square minimization procedure. We study separately summer and annual dynamics. When we use the models to reproduce annual dynamics, we include a simple representation of the annual cycle of evapotranspiration. We test the models both in simulation mode, estimating their parameters from the same data used to verify them, and in forecast mode, determining the model parameters from one period, and using them to forecast soil water dynamics in a different period. The results indicate that simple box models can estimate soil water dynamics at midlatitudes, using rainfall as the only meteorological driver. The models displaying the best performances include the representation of leakage and evapotranspiration as nonlinear functions of soil water content.

Experimental evaluation of the hydrodynamic coefficients of a ROV through Morison’s equation

The determination of hydrodynamic coefficients of full-scale ROV using system identification (SI) is an extremely powerful technique. The procedure is based on experimental runs and on the analysis of on-board sensors and thrusters signals. The technique is cost effective and it has high repeatability; however, it lacks accuracy due to the sensors noise and the poor modeling of thruster–hull and thruster–thruster interaction effects. In this work, forced oscillation tests using a planar motion mechanism (PMM) were undertaken with a full-scale open-frame ROV. These tests are unique in the sense that there are not many examples in the literature taking advantage of a PMM installation for testing a prototype and, consequently, allowing the comparison between the experimental results and the ones estimated by SI. The Morison equation inertia and drag coefficients were estimated with two parameter identification methods that are the weighted and the ordinary least-squares procedures. Error analysis showed that the ordinary least-squares provided better accuracy and, therefore, was used to evaluate the ratio between inertia and drag forces for a range of Keulegan–Carpenter and Reynolds numbers. The research provided a rich amount of reference data for comparison with reduced models as well as for ROV dynamic motion simulation.

A Method of Reliability Sensitivity Analysis for Gear Drive System

Based on profile involutes equation and tooth easement curve equation of standard gear, parameterization three dimensional finite element model of the gear drive system is built up in ANSYS, and numerical computation of the working process is taken in ANSYS/LS-DYNA, then contact stress of and pressure distribution are got. It creates an ultimate state equation of every system parameter (input) converting to output (response), considering different system random error synthetically, sample points locations in input variable sampling space are fixed with the method of matrix experiment design, which was used in series of deterministic fitting test. In the test, least-squares procedure regression analysis of the ultimate state equation is taken to fix the items and coefficients after multiple fitting test. Using this ultimate state equation, system reliability level and reliability sensitivity of different variables can be calculated which provides theoretical bases for dynamic optimum design of gear drive system.

WAVELENGTHS, ENERGY LEVELS, LIFETIMES, AND WEIGHTED OSCILLATOR STRENGTHS FOR THE S VIII SPECTRUM

The weighted oscillator strengths (gf) and lifetimes for S VIII presented in this work were obtained by a multiconfigurational Hartree-Fock relativistic approach. In this calculation, the electrostatic energy parameters were optimized by a least-squares procedure in order to improve the adjustment to experimental energy levels. The values for gf and lifetimes were then calculated on the basis of these adjusted parameters. New classifications are proposed for energy levels belonging to the 4s and 4d configurations and lines related to them.

Parameter identification of multibody systems based on second order sensitivity analysis

An identification procedure for multibody systems is presented to determine optimal values for unknown or estimated model parameters from experimental test data. Based on a non-linear least-square optimization procedure, the Levenberg–Marquardt trust region method is developed to estimate the unknown parameters, in which the second order sensitivity analysis with the hybrid method is applied to improve the convergence and stability. Finally, numerical examples of slider-crank mechanism validate the accuracy and efficiency of the method presented.

A New Method for Identifying the Cutter Runout Parameters in Flat End Milling Process

Cutter runout will redistribute the instantaneous uncut chip thickness and the cutting forces in multi-fluted milling process. In this paper, a new procedure is proposed to identify the cutter runout parameters for flat end milling process. By combining least-square method, mathematical derivations and implementation procedures are carried out based on the relative deviation between each cutting edge and the spindle rotation center, measured by a dial gauge. Numerical verifications are conducted to validate the proposed procedures, and the results show that they are efficient and reliable. It is also suggested that to weaken the influence of noise signal, measurements should be conducted at multiple axial positions.

Determination of Silicon in Lubricant Oil by High-Resolution Continuum Source Flame Atomic Absorption Spectrometry Using Least-Square Background Correction and Internal Standardization

The least-squares background correction (LSBC) and internal standardization procedures were combined to eliminate spectral interferences caused by the CS molecular band (251.602 nm) and transport effects for determining Si in sulfuric acid digests of lubricant oil by high-resolution continuum source flame atomic absorption spectrometry. Aluminum, Ba, Ti, V, and W were tested as internal standard (IS) candidates, and W provided the best results. For absorbance measurements of solutions containing 0.5–5.0 mg L−1 Si in the presence of 25 mg L−1 W (at the wavelength integrated absorbance equivalent to 3 pixels), the correlation coefficient for the ratio of absorbance of Si to absorbance of W vs. analyte concentration was 0.9978. Fluctuations in analytical signals due to variations in sulfuric acid concentrations or acetylene/nitrous oxide flow-rate ratios were corrected by using this calibration plot. Relative standard deviations varied from 1.9 to 7.2% and 2.1 to 5.4% (n = 12) with and without LSBC/IS, respectively. Recoveries for samples spiked with 2.0 mg L−1 Si in 5.0% (v/v) sulfuric acid were within the 72.5–82.5% and 94.0–99.0% ranges without correction and by LSBC associated with internal standardization procedure, respectively. Accuracy of the proposed method was checked for the determination of Si in commercial lubricant oils and results obtained with internal standardization were better than those without correction.

Doppler-limited spectroscopy of the A3Π 1 ← X1Σ + system of ICl in the 0.8 μm region using a Ti:sapphire ring laser

Doppler-limited vib-rotational absorption spectra of the A ← X electronic transition of I 35/37Cl are measured in the range 11,352–13,507 cm −1 using a Ti:sapphire ring laser. The P-, Q-, and R-branch lines belonging to the v ← v″ = (0–7) ← (0–7) transition in I 35Cl and the v ← v″ = (0–6) ← (2–6) transition in I 37Cl are assigned. Under Doppler-limited conditions, the P- and R-branch lines are split into doublets by the nuclear quadrupole coupling effect of the I atom. The unperturbed positions of these lines are correctly calculated, whereas splitting in the Q-branch lines was not observed. The mass-reduced Dunham expansion coefficients U l, m of the A and X states and the spectroscopic constants T v ′ , B v ′ e / f , D v ′ , and H v ′ of the A state are determined using a global least-squares fitting procedure.

Comparative metabolic rates of common western North Atlantic Ocean sciaenid fishes

The resting metabolic rates (R(R)) of western North Atlantic Ocean sciaenids, such as Atlantic croaker Micropogonias undulatus, spot Leiostomus xanthurus and kingfishes Menticirrhus spp., as well as the active metabolic rates (R(A)) of M. undulatus and L. xanthurus were investigated to facilitate inter and intraspecific comparisons of their energetic ecology. The R(R) of M. undulatus and L. xanthurus were typical for fishes with similar lifestyles. The R(R) of Menticirrhus spp. were elevated relative to those of M. undulatus and L. xanthurus, but below those of high-energy-demand species such as tunas Thunnus spp. and dolphinfish Coryphaena hippurus. Repeated-measures non-linear mixed-effects models were applied to account for within-individual autocorrelation and corrected for non-constant variance typical of noisy R(A) data sets. Repeated-measures models incorporating autoregressive first-order [AR(1)] and autoregressive moving average (ARMA) covariances provided significantly superior fits, more precise parameter estimates (i.e. reduced s.e.) and y-intercept estimates that more closely approximated measured R(R) for M. undulatus and L. xanthurus than standard least-squares regression procedures.

Modelling of Cyclic Plasticity and Viscoplasticity of Directionally Solified DZ125 Superalloy: Part I: Estimating the Parameters of Chaboche Constitutive Equations

Cyclic plasticity and viscoplasticity of directionally solified superalloy, DZ125, have been described using the Chaboche unified constitutive model. A set of initial material parameters has been determined utilizing the monotonic, cyclic, relaxation and creep test data of DZ125 at 980°C, while an optimum set of material parameters has been obtained by means of least-square procedure.

Denoising two-photon calcium imaging data.

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.

Studies in mice, hamsters, and rats demonstrate that repression of hepatic apoA-I expression by taurocholic acid in mice is not mediated by the farnesoid-X-receptor

It is claimed that apoA-I expression is repressed in mice by cholic acid (CA) and its taurine conjugate, taurocholic acid (TCA) via farnesoid X receptor (FXR) activation. We measured apoA-I expression in mice, hamsters, and rats treated with highly potent and selective synthetic FXR agonists or with TCA. All of the synthetic agonists bound to FXR with high affinity in a scintillation proximity assay. However, TCA did not compete with the radioligand up to the highest concentration used (100 μM). The C-site regulatory region of apoA-I, through which FXR has been reported to regulate its expression, is completely conserved across the species investigated. In both male and female human apoA-I-transgenic mice, we reproduced the previously reported strong inhibition of human apoA-I expression upon treatment with the typical supraphysiological dose of TCA used in such studies. However, in contrast to some previous reports, TCA did not repress murine apoA-I expression in the same mice. Also, more-potent and -selective FXR agonists did not affect human or murine apoA-I expression in this model. In LDL receptor-deficient mice and Golden Syrian hamsters, selective FXR agonists did not affect apoA-I expression, whereas in Wistar rats, some even increased apoA-I expression. In conclusion, selective FXR agonists do not repress apoA-I expression in rodents. Repression of human apoA-I expression by TCA in transgenic mice is probably mediated through FXR-independent mechanisms.

Solubilities of salts in the ternary systems NaCl + CaCl2 + H2O and KCl + CaCl2 + H2O at 75°C

The solubility in the NaCl-CaCl2-H2O and KCl-CaCl2-H2O systems were determined at 75°C and the phase diagrams and the diagram of physicochemical property vs composition were plotted. One invariant point, two univariant curves, and two crystallization zones, corresponding to potassium chloride, dihydrate (CaCl2 · 2H2O) showed up in the phase diagrams of the ternary systems. The mixing parameters θM, Ca and ΨM, Ca, Cl (M = Na or K) and equilibrium constant Ksp were evaluated in NaCl-CaCl2-H2O and KCl-CaCl2-H2O systems by least-squares optimization procedure, in which the single-salt Pitzer parameters of NaCl, KCl, and CaCl2 β(0), β(1), β(2), and CΦ were directly calculated from the literature. The results obtained were in good agreement with the experimental data.

Separation of blended data by iterative estimation and subtraction of blending interference noise

Seismic acquisition is a trade-off between economy and quality. In conventional acquisition the time intervals between successive records are large enough to avoid interference in time. To obtain an efficient survey, the spatial source sampling is therefore often (too) large. However, in blending, or simultaneous acquisition, temporal overlap between shot records is allowed. This additional degree of freedom in survey design significantly improves the quality or the economics or both. Deblending is the procedure of recovering the data as if they were acquired in the conventional, unblended way. A simple least-squares procedure, however, does not remove the interference due to other sources, or blending noise. Fortunately, the character of this noise is different in different domains, e.g., it is coherent in the common source domain, but incoherent in the common receiver domain. This property is used to obtain a considerable improvement. We propose to estimate the blending noise and subtract it from the blended data. The estimate does not need to be perfect because our procedure is iterative. Starting with the least-squares deblended data, the estimate of the blending noise is obtained via the following steps: sort the data to a domain where the blending noise is incoherent; apply a noise suppression filter; apply a threshold to remove the remaining noise, ending up with (part of) the signal; compute an estimate of the blending noise from this signal. At each iteration, the threshold can be lowered and more of the signal is recovered. Promising results were obtained with a simple implementation of this method for both impulsive and vibratory sources. Undoubtedly, in the future algorithms will be developed for the direct processing of blended data. However, currently a high-quality deblending procedure is an important step allowing the application of contemporary processing flows.

Estimating cost‐offsets of new medications: Use of new antipsychotics and mental health costs for schizophrenia

Estimation of the effect of one treatment compared to another in the absence of randomization is a common problem in biostatistics. An increasingly popular approach involves instrumental variables—variables that are predictive of who received a treatment yet not directly predictive of the outcome. When treatment is binary, many estimators have been proposed: method-of-moments estimators using a two-stage least-squares procedure, generalized-method-of-moments estimators using two-stage predictor substitution or two-stage residual inclusion procedures, and likelihood-based latent variable approaches. The critical assumptions to the consistency of two-stage procedures and of the likelihood-based procedures differ. Because neither set of assumptions can be completely tested from the observed data alone, comparing the results from the different approaches is an important sensitivity analysis. We provide a general statistical framework for estimation of the casual effect of a binary treatment on a continuous outcome using simultaneous equations to specify models. A comparison of health care costs for adults with schizophrenia treated with newer atypical antipsychotics and those treated with conventional antipsychotic medications illustrates our methods. Surprisingly large differences in the results among the methods are investigated using a simulation study. Several new findings concerning the performance in terms of precision and robustness of each approach in different situations are obtained. We illustrate that in general supplemental information is needed to determine which analysis, if any, is trustworthy and reaffirm that comparing results from different approaches is a valuable sensitivity analysis. Copyright © 2011 John Wiley & Sons, Ltd.

Synthesis and Crystal Structure of (2S,6R) Ethyl 1,2,6-triphenyl-4-(phenylamino)-1,2,5,6-tetrahydropyridine-3-carboxylate

The title compound, (2S,6R), Ethyl 1,2,6-triphenyl-4-(phenylamino)-1,2,5,6-tetrahydropyridine-3-carboxylate (C32H30N2O2), was synthesised by the reaction of benzaldehyde, aniline and ethylacetoacetate, in the presence of l (−) proline–Fe(III) complex, formed in situ, at room temperature. The compound was characterized by spectral methods and X-ray diffraction studies. The compound crystallizes in the triclinic space group P − 1 with the following unit-cell parameters: a = 9.651(4), b = 10.909(5), c = 13.737(7) A, α = 106.597(7), β = 108.664(8), γ = 99.779(6)°, Z = 2. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at 100 K and refined by full-matrix least-squares procedures to a final R-value of 0.0633 for 3415 observed reflections. The 1,2,5,6-tetrahydropyridine ring exhibits a flat boat conformation. The structure has intra- and intermolecular hydrogen bonds of the type N–H···O, C–H···O and C–H···π, which help to stabilize the crystal structure. Crystal structure analysis of (2S,6R) Ethyl 1,2,6-triphenyl-4-(phenylamino)-1,2,5,6-tetrahydropyridine-3-carboxylate.