In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators. 相似文献
Objective: The aim of this study was to investigate the whole spine alignment in automotive seated postures for both genders and the effects of the spinal alignment patterns on cervical vertebral motion in rear impact using a human finite element (FE) model.
Methods: Image data for 8 female and 7 male subjects in a seated posture acquired by an upright open magnetic resonance imaging (MRI) system were utilized. Spinal alignment was determined from the centers of the vertebrae and average spinal alignment patterns for both genders were estimated by multidimensional scaling (MDS). An occupant FE model of female average size (162 cm, 62 kg; the AF 50 size model) was developed by scaling THUMS AF 05. The average spinal alignment pattern for females was implemented in the model, and model validation was made with respect to female volunteer sled test data from rear end impacts. Thereafter, the average spinal alignment pattern for males and representative spinal alignments for all subjects were implemented in the validated female model, and additional FE simulations of the sled test were conducted to investigate effects of spinal alignment patterns on cervical vertebral motion.
Results: The estimated average spinal alignment pattern was slight kyphotic, or almost straight cervical and less-kyphotic thoracic spine for the females and lordotic cervical and more pronounced kyphotic thoracic spine for the males. The AF 50 size model with the female average spinal alignment exhibited spine straightening from upper thoracic vertebra level and showed larger intervertebral angular displacements in the cervical spine than the one with the male average spinal alignment.
Conclusions: The cervical spine alignment is continuous with the thoracic spine, and a trend of the relationship between cervical spine and thoracic spinal alignment was shown in this study. Simulation results suggested that variations in thoracic spinal alignment had a potential impact on cervical spine motion as well as cervical spinal alignment in rear end impact condition. 相似文献
Distribution of pollutants in coastal waters is usually represented by depth averaged twodimensional convection-dispersion equation. Under very specific conditions this equation can be solved analytically. Although such a solution is restricted to simplified situations it provides a very useful case for testing the performance of various numerical solution techniques currently available for the simulation of convective-dispersion of pollutants in natural water systems. In this paper the analytical solution of the convective dispersion equation is used as a benchmark against which the accuracy of other techniques are assessed. These assessments are based on quantitative comparisons between the results of the solution of two-dimensional convection-dispersion equation by the deterministic finite element and stochastic random walk methods. Both Eulerian and Lagrangian frameworks are employed to obtain the finite element solution of the convection-dispersion problem. It has been shown that the Lagrange–Galerkin finite element scheme yields the most accurate results for the case under study. However, computational costs of the Lagrange–Galerkin method can be relatively high and under certain conditions it may be reasonable to use a less accurate but cost effective random walk scheme to make water quality management decisions. 相似文献