The Effectiveness of the Havriliak-Negami Model in Predicting the Master Curves of the Asphalt Blends with SBS Triblock Copolymer and Organic-Montmorillonite at Different Temperatures and Frequencies

The dynamic viscoelastic properties of asphalt AC-20 and its composites with Organic-Montmorillonite clay (OMMt) and SBS were modeled using the empirical Havriliak-Negami (HN) model, based on linear viscoelastic theory (LVE). The HN parameters, α, β, G0, G∞and τHN were determined by solving the HN equation across various temperatures and frequencies. The HN model successfully predicted the rheological behavior of the asphalt and its blends within the temperature range of 25˚C - 40˚C. However, deviations occurred between 40˚C - 75˚C, where the glass transition temperature Tg of the asphalt components and the SBS polymer are located, rendering the HN model ineffective for predicting the dynamic viscoelastic properties of composites containing OMMt under these conditions. Yet, the prediction error of the HN model dropped to 2.28% - 2.81% for asphalt and its mixtures at 100˚C, a temperature exceeding the Tg values of both polymer and asphalt, where the mixtures exhibited a liquid-like behavior. The exponent α and the relaxation time increased with temperature across all systems. Incorporating OMMt clay into the asphalt blends significantly enhanced the relaxation dynamics of the resulting composites.

Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

ADMISSIBILITY OF LINEAR ESTIMATORS IN A GROWTH CURVE MODEL SUBJECT TO AN INCOMPLETE ELLIPSOIDAL RESTRICTION

This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.

Comparative Study on Analysis and Fitting of Pudong Chicken Growth Curve

The objective of this paper was to study the growth and development laws of Pudong chicken. The growth curve of Pudong chicken （cock and hen） from 0 to 20 weeks was analyzed and fitted with three models（Gompertz, Logistic and Bertalanffy）. It was concluded that the growth curves were appropriately fitted with three models, and fitness degree （R2）in growth data of Pudong chicken were all above 0.992. The Bertalanffy model was the most effective with the highest R2 for cock （R^2=0.995） and hen （R^2=0.999）, respectively. With further analysis of fitted parameters for Logis- tic model of cock, 0-3 weeks＇ fitted values were significantly greater than measured values and 4-8 weeks＇ fitted values were lower than measured values. Compared with Logistic model, the values calculated by Gompertz model and Bertalanffy model were more coincident with the practical measuring values. For hens, 0-3 weeks＇ fitted values of Logistic model were significantly greater than measured values and 0-2 weeks＇ fitted values of Gompertz model were slightly greater than measured values, while the values calculated by Bertalanffy model best matched the observed values from actual measure. The results showed that Bertalanffy model used to estimate the growth weight of Pudong chicken was the best while Logistic model was the worst. So the fitness and analysis of growth curves of Pudong chicken are valid, which may be adopted to predict growth and development laws of Pudong chicken and provide reliable data for precise feeding and breeding.

A NEW APPROACH TO THE CURVE FITTING OF IN VITRO RADIOASSAYS BASED ON THE MASS ACTION LOW

A new curve fitting method with its mathematical models derived from the mass action law is presented which is applicable to several in vitro radioassays including RIA and RBA. Experiments revealed that the robustness of this method is better than the conventional methods like Woolf plot in RBA and 4- parameter logistic plot in RIA. However, the robustness of this method is only relative: in some cases of RIA and RBA, the bias of the results may still be too large to be acceptable. Further improvement is expected to be studied.

Least squares fitting of coordinate parameters model

This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model. The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model. During discussion, the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.

Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam

Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling.The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points,and to get high-quality parametric model for isogeometric analysis.ATimoshenko beam element is established for an initially curved spacial beam with arbitrary curvature.The approximation and interpolation methods to get parametric models of curves from given points are examined,and three strategies of parameterization,meaning the equally spaced method,the chord length method and the centripetal method are considered.The influences of the different geometric approximation algorithms on the precision of isogeometric analysis are examined.The static analysis and the modal analysis with the established parametric models are carried out.Three examples with different complexities,the quarter arc curved beam,the Tschirnhausen beam and the Archimedes spiral beam are examined.The results show that for the geometric approximation the interpolation method performs good and maintains high precision.The fitting algorithms are able to provide parametric models for isogeometric analysis of spacial beam with Timoshenko model.The equally spaced method and centripetal method perform better than the chord length method for the algorithm to carry out the parameterization for the sampling points.

GENERAL ADMISSIBLE LINEARESTIMATORS IN RESTRICEDGROWTH CURVE MODEL

In this paper, we give a class of fuation and use to dicuss general admissibility according to general optimality ceriteria defined uader restricted growth curve model. General admissible characterization are obtained. Moreover, these conditions are then utilize to characterize infulueace that restrictions involved in growth curve model have on the class of admissible linear

基于自适应AR模型巡航飞行参数预测研究

为更准确实现飞行参数趋势预测,提出一种基于自适应自回归(AR)模型的稳定巡航飞行参数预测方法。根据稳定巡航参数筛选条件,获取建模所需飞行参数。利用卡尔曼滤波原理估计AR模型参数,并与飞行参数构建系统方程,利用无迹卡尔曼滤波实时更新、修正AR模型参数估计值,将自适应AR模型的预测值与曲线拟合模型和灰色模型的预测值进行对比。以波音B777-300ER飞机的快速存取记录器数据样本进行仿真验证,结果表明:自适应AR模型在数据预测和收敛速率方面均更优,可有效降低预报模型随步数增加导致的精度误差,提高参数预测准确性。研究在飞机维修保障、状态监控与预测等方面具有重要作用。

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

Comparative Study on Growth and Developmental Model of Indigenous Chicken Breeds in China

The growth and development regularity and genetic parameters were described in three types of indigenous chicken in China, Shaobo, Huaixiang and Youxi Chicken, by 3 nonlinear mathematics models, Logistics, Gompertz and Bertalanfy, according to the data of Body Weight from 1 week to 10 weeks. The results showed that the growth process of the three breeds could be illustrated well by three models, and the indices of fitness were very high (more than 0.99). Among the 3 models, Gompertz model was the best for its less bias from practice. The inflexions of growth were 5.98, 5.11 and 6.16 weeks of age, and body weights were 2115.77 g, 1499.08 g and 1409.62 g, respectively in Shaobo Chicken, Huaixiang Chicken and Youxi Chicken.

A fault recognition method based on clustering linear regression

Aiming at the problems of low accuracy,long time consumption,and failure to obtain quantita-tive fault identification results of existing automatic fault identification technic,a fault recognition method based on clustering linear regression is proposed.Firstly,Hough transform is used to detect the line segment of the enhanced image obtained by the coherence cube algorithm.Secondly,the endpoint of the line segment detected by Hough transform is taken as the key point,and the adaptive clustering linear regression algorithm is used to cluster the key points adaptively according to the lin-ear relationship between them.Finally,a fault is generated from each category of key points based on least squares curve fitting method to realize fault identification.To verify the feasibility and pro-gressiveness of the proposed method,it is compared with the traditional method and the latest meth-od on the actual seismic data through experiments,and the effectiveness of the proposed method is verified by the experimental results on the actual seismic data.

Parametric Study of Low Frequency Broadband Rectilinear-to-Rotary Vibrational Energy Harvesting

A parametric study of a high-power-density dual resonator for achieving low frequency broadband electromagnetic energy harvesting is reported.The dual resonator consists of a rectilinear oscillator(R_LO)performing magnetic levitation and a rotary oscillator(R_TO)performing electromagnetic coupling through a stator and a rotor.Both oscillators,coupled by magnetic forces generated by a set of arc permanent magnets,radially magnetized and centro-symmetrically fixed onto the R_LO and the rotor of the R_TO achieve the reciprocating-to-rotary motion conversion and frequency up-conversion.Specifically,the dual resonator is able to convert stochastic reciprocating motion into controllable rotation,provide intrinsic frequency up-conversion,use non-contact magnetic coupling to provide near loss-free energy transfer and be configured into specific applications to obtain and maintain high-energy orbits of multi-stable energy harvesting.While solely focusing on developing a dual resonator provides substantial benefits,its dynamic behavior is unclear,thus electromagnetic-dynamic governing equations are derived,and a curve fitting model of restoring torque of R_TO under different repulsive magnets configurations are developed to predict key characteristics and to improve performance of the electromechanical system.Power analysis is carried out for providing aquantitative guidance of customizing the harvester to achieve an optimal power density.

ADMISSIBILITY IN THE GENERAL GROWTH CURVE MODEL WITH RESPECT TO RESTRICTED PARAMETER SETS UNDER MATRIX LOSS FUNCTION

In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively.

Applications of Chapman-Richards model to geotechnical engineering

In this paper,the Chapman-Richards model is adapted to best fit three types of nonlinear curves that are generally encountered in geotechnical engineering practices,i.e.the degree of consolidation versus time factor curves in one-dimensional consolidation and plane strain consolidation under strip loading,the compressibility and permeability curves of soft clay,and the geometry parameters of geosynthetic tube versus pumping pressure curves.The methods of determining unknown parameters using the Chapman-Richards model are fully demonstrated.It is found that the Chapman-Richards model has its range of applications in geotechnical engineering and may provide unique insights into the complexity of geotechnical problems.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

Hybrid reliability model for fatigue reliability analysis of steel bridges

A kind of hybrid reliability model is presented to solve the fatigue reliability problems of steel bridges. The cumulative damage model is one kind of the models used in fatigue reliability analysis. The parameter characteristics of the model can be described as probabilistic and interval. The two-stage hybrid reliability model is given with a theoretical foundation and a solving algorithm to solve the hybrid reliability problems. The theoretical foundation is established by the consistency relationships of interval reliability model and probability reliability model with normally distributed variables in theory. The solving process is combined with the definition of interval reliability index and the probabilistic algorithm. With the consideration of the parameter characteristics of the S-N curve, the cumulative damage model with hybrid variables is given based on the standards from different countries. Lastly, a case of steel structure in the Neville Island Bridge is analyzed to verify the applicability of the hybrid reliability model in fatigue reliability analysis based on the AASHTO.

High Order Tensor Forms of Growth Curve Models

In this paper, we first study the linear regression model and obtain a norm-minimized estimator of the parameter vector by using the g-inverse and the singular value decomposition of matrix X. We then investigate the growth curve model (GCM) and extend the GCM to a generalized GCM (GGCM) by using high order tensors. The parameter estimations in GGCMs are also achieved in this way.

函数系数自回归模型推广形式的Back-Fitting估计

文章针对时间序列中函数系数自回归模型给出其推广形式,借助向后拟合的思想介绍推广形式中函数系数部分和参数部分的估计,该方法可以得到模型中的常值系数估计量的精确表达式;并通过一个数值模拟表明所提出的估计方法具有可行性和稳定性。

线性测量误差模型的lack-of-fit检验

基于正态假设 ,提出了测量误差模型lack of fit检验的一种方法 .在原假设下 ,检验统计量渐近服从 χ2 分布 .还就该检验的势函数与权函数的选择进行了讨论 。