LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

Study on Growth and Development Rules and Growth Curve Fitting of Minghua Black Minks

Growth curves of Minghua black minks at 0-180 days old were fitted and analyzed by using two growth models Logistic and Gompertz. The results showed that the growth curves of Minghua black minks could be fitted very well by Logistic model and Gompertz model （the degree of fitting FF≥0.99）, but Gompertz model was better at fitting and predicting their weight.

The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares Fitting System

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.

A unified approach for least-squares surface fitting

This paper presents a novel approach for least-squares fitting of complex surface to measured 3D coordinate points by adjusting its location and/or shape. For a point expressed in the machine reference frame and a deformable smooth surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion and differential deformation of the surface is derived. On this basis, localization, surface reconstruction and geometric variation characterization are formulated as a unified nonlinear least-squares problem defined on the product space SE(3)×Km. By using Levenberg-Marquardt method, a sequential approximation surface fitting algorithm is developed. It has the advantages of implementational simplicity, computational efficiency and robustness. Applications confirm the validity of the proposed approach.

DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

Effects of dietary protein levels on the long-term growth response and fitting growth models of gibel carp(Carassius auratus gibelio)

A 41-wk growth trial was conducted to evaluate the effects of dietary protein levels on the long-term growth response and fitting growth models of gibel carp(Carassius auratus gibelio) with an initial body weight of 1.85 ± 0.17 g. The dietary protein levels were designed at 320(P32), 360(P36). 400(P40).and 440 g/kg(P44), respectively. The growth curves of the gibel carp for each group were fitted and analyzed with four nonlinear regression models(Gompertz. logistic. von Bertalanffy and Richards). The final body weights(mean ± SD) of the fish were 226 ± 6.231 ± 7.242 ± 2, and 236 ± 2 g for P32, P36, P40,and P44. respectively. Feed conversion ratio of P40 and P44 groups was significantly lower than that of P32 and P36 groups(P < 0.05). Productive protein value of P44 group was significantly lower than that of P32 and P36 groups, but not different from that of P40 group(P > 0.05). The growth response of the gibel carp for each group was the best fitted by Richards model with the lowest Chi^2, residual sum of squares and residual variance, then Gompertz and von Bertalanffy growth models, but the logistic model did not fit the data well justified by Chi^2 values. The optimal protein level(400 g/kg) prolonged the stage of fast growth and predicted the highest asymptotic weight, which was close to the harvest size in practice.

Formulation of Reduction Rate for Ultimate Compressive Strength of Stiffened Panel Induced by Opening

The main objective of this study is to numerically investigate the characteristics of ultimate compressive strength of stiffened panels with opening and also to fit the design-oriented formulae. For this purpose, three series of well executed experimental data on longitudinally stiffened steel plates with and without opening subjected to the uniform axial in-pane load which is carried out to study the buckling and post-buckling up to the final failure are chosen. Also, a nonlinear finite element method capable of efficiently analyzing the large elasto-plastic deflection behavior of stiffened panels is developed and used for simulation. The feasibility of the present simulation process is confirmed by a good agreement with the experimental results. More case studies are developed employing the simulation process to analyze the influence of various design variables on the reduction rate of ultimate strength of stiffened panel induced by opening. Based on the computed results, two design formulae are fitted and the accuracy of design formulae is studied. Furthermore, the viability of the design formulae for practical engineering is proved.

Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method

With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.

Baseline correction for digital strong-motion records by using the pre-event portion

Baseline offset in digital strong-motion acceleration record and initial velocity can produce unrealistic results for ground velocity and displacement derived from the acceleration by integration. A new method is proposed for the baseline correction and initial velocity calculation. It is based on linear least-squares fitting of the pre-event portion of velocity derived from the uncorrected acceleration data. Compared with the conventional method,which is based on removing the mean values of the pre-event portions of the acceleration and velocity traces,this method has clearer physical meaning and better stability.

Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis

This paper presents the isogeometric least-squares collocatio method,which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense.The number of collocation points employed in IGA-L can be larger than that of the unknowns.Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods.First,a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution.Second,IGA-L method is more flexible and more stable,because the number of collocation points in IGA-L is variable.Third,IGA-L is convergent in some cases of singular parameterization.Moreover,the consistency and convergence analysis are also developed in this paper.

Gas flow and filter ventilation of an unlit cigarette: model building,numerical solution and experimental validation

Understanding the fundamcntal relationship betwecn gas dilution rate of a cigarette and key cigarette design parameters is important in the overall control of smoke yield.In this work,an equation was derived to express the total gas dilution with the cigarette rod length,cigarette paper air permeability,and the filter ventilation level.The relationship was validated using experimental results.The accuracy of the developed model was dependent on the regression method used,i.e.,linear or a nonlinear.The expression provides a quantitative description of the interactions between filter ventilation level,cigarette length,cigarette circumference and cigarette paper air permeability and the total air dilution at the cigarette's mouth end.

Pyrolysis Characteristics and Kinetics of Municipal Solid Waste

Based on a systemic survey, the pyrolysis characteristics and apparent kinetics of the municipal solid waste （ MSW） under different conditions were researched using a special pyrolysis reactor, which could overcome the disadvantage of thermo-gravimetric analyzer. The thermal decomposition behaviour of MSW was investigated using thermo-gravimetric （ TG ） analysis at rates of 4.8,6.6,8.4, 12.0 and 13. 2 K/min. The pyrolysis characteristics of MSW were also studied in different function districts. The pyrolysis of MSW is a complex reaction process and three main stages are found according to the results. The first stage represents the degradation of cellulose and hemicellulose, with the maximum degradation rate occuring at 150℃ -200 ℃： the second stage represents dehydrochlorination and depolymerization of intermediate products and the differential thermogravimetric （ DTG ） curves have shoulder peaks at about 300℃： the third stage is the decomposition of the residual big molecular organic substance and lignin at 400 ℃- 600 ℃. Within the range of given experimental conditions, the results of non-linear fitting algorithm and experiment are in agreement with each other and the correlation coefficients are over0. 99. The kinetic characteristics are concerned with the material component and heating rate. The activation energy of reaction decreases with the increase of heating rate.

Study on the Shear Effect on Dye Patches Diffused in Wall-Bounded Shear Flow

This paper focuses on the high intensity filaments (dye patches) embedded in dye plumes in a wall-bounded shear flow, to investigate the shear effect on the dye patch distribution. Motivated by the widely concerned inverse estimation of the source location, we try extracting useful information to know the source location from down-stream dye patches. Accordingly, we changed the dye injection location at different distances from the wall and made observations at different downstream (diffusion) distances from the source. The orientation angle and roundness of dye patches were concerned to examine the shear effect and dye patch characteristics. To capture the dye plume images, a planar laser induced fluorescence (PLIF) technique was used. The orientation and roundness of each dye patch were calculated by least-square fitting. The statistics of both the orientation angle and the roundness were compared with those in homogeneous turbulent cases to reveal the shear effect. Different from uniformly-orientated dye patches in the homogeneous flow, larger occurrence probabilities with positive orientation angles of dye patches are observed in wall-bounded shear flow, in particular, when the injection location is near the wall. As with information extraction for the inverse estimation of source location, it is found that the orientation distribution of dye patches is independent of the diffusion distance, but related with the injection location from the wall. While for the homogeneous flow cases, a strong dependence on the diffusion distance is observed in the orientation distribution profiles. As for the roundness, similar aspects are found regarding the dependencies on the injection location in shear flow and on diffusion distance in homogeneous flow.

Equilibrium dialysis study on the interaction between Cu(Ⅱ) and HSA or BSA

The interaction of Cu(Ⅱ) and human serum albumin (HSA) or bovine serum albumin (BSA) at physiological pH is studied by equilibrium dialysis. The successive stability constants are obtained by non-linear least square methods fitting Bjerrum formula. For both the Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, the order of magnitude of K 1 and K 2 was found to be ≈10 4 mol -1·dm 3. There are about twenty stoichiometry binding sites found in one HSA or BSA molecule. They can be divided into two or three sets. Results of equilibrium dialysis experiments suggest that there exists one strong metal binding site in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA. It is the imidazol group nitrogen atoms of His 3 that are primarily concerned with copper binding site. After reaching dialysis equilibrium, there is the interaction among the different binding sites, the values of K all deviate from the simple statistical effect except for K-1 and K-2 in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, and the positive cooperative effect is found.

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.

Beam induced vacuum measurement error in BEPC II

When the beam in BEPCII storage ring aborts suddenly, the measured pressure of cold cathode gauges and ion pumps will drop suddenly and decrease to the base pressure gradually. This shows that there is a beam induced positive error in the pressure measurement during beam operation. The error is the difference between measured and real pressures. Right after the beam aborts, the error will disappear immediately and the measured pressure will then be equal to real pressure. For one gauge, we can fit a non-linear pressure-time curve with its measured pressure data 20 seconds after a sudden beam abortion. From this negative exponential decay pumping-down curve, real pressure at the time when the beam starts aborting is extrapolated. With the data of several sudden beam abortions we have got the errors of that gauge in different beam currents and found that the error is directly proportional to the beam current, as expected. And a linear data-fitting gives the proportion coefficient of the equation, which we derived to evaluate the real pressure all the time when the beam with varied currents is on.

MODELING STRATEGIES FOR CONTROLLING H1N1 OUTBREAKS IN CHINA

There has been a global attack of A/H1N1 virus in 2009, which widely affected the world＇s normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 May 2009 in China, very strict policy including quarantine and isolation measures were widely implemented to control the spread of this disease before the vaccine appeared. We propose a compartmental model that mimics the infection process of A/H1N1 under control strategies taken in China's Mainland. Apart from theoretical analysis, using the statistic data of Shaanxi Province, we estimated the unknown epidemiological parameters of this disease in Shaanxi via least-squares fitting method. The estimated control reproductive number of H1N1 for its first peak was Rc1 = 2.555 （95% CI： 2.362 2.748） and that for the second peak was Rc2 = 1.886 （95% CI： 1.765-2.001）. Our findings in this paper suggest that neither quarantine nor isolation measures could be relaxed, and the implementation of these interventions can reduce the pandemic outbreak of A/H1N1 pandemic significantly.