Imperfect Frame Research Articles

Census 2000--Science Meets Politics

T he Supreme Court has ruled that it is illegal to use statistical sampling to provide population counts for congressional reapportionment. Should scientists other than statisticians, demographers, and political scientists bother to follow the strange politics that have engulfed Census 2000? Yes, as a warning about how partisanship can affect a scientific agency. The census began as the result of the great political compromise that founded the United States. If congressional power was to be apportioned geographically (satisfying small states) and proportionate to size (satisfying large states), regular measurement of the number and distribution of residents was a necessity. In the 19th century, census results regulated the pace for admitting new states to the union, as partisan interests took turns vying for advantage. In 1920, the census measured a population shift from rural to urban states so alarming to Congress that it postponed for a decade its constitutional obligation to reapportion. But past politics focused mostly on how census results were to be used. Today's battle has been broadened to focus on how data will be collected. Technical decisions (for example, on how many census forms to mail) normally made by career professionals are today routinely reviewed by an oversight apparatus intent on influencing how the census will be conducted. Regrettably, the division of views falls along partisan lines. Even the Supreme Court divided along conservative and liberal lines in its recent decision. Science by partisan vote is a risky enterprise. The Census Bureau takes as much professional pride in accurately reporting how inaccurate it is as it does in trying to be completely accurate in the first place. We know that we miss people in our decennial count, and we know that this undercount is unevenly distributed demographically and geographically. This knowledge comes from our own post-census quality survey. The quality survey we recommend for Census 2000 is under attack because of its potential use for drawing legislative districts in 2001. Such use is an altogether appropriate issue for resolution in the political-legal arena. But other critical uses should not be compromised. To discard the quality survey would take away the science by which we assess our performance; we could not then tell the public whether census procedures in 2000 improved on those used in 1990. Planning for the next census would be crippled. Moreover, for at least a decade, statistical surveys of any kind would be based on an imperfect sampling frame and error-prone sampling weights. Just as there can be reasonable differences among lawyers about the interpretation of the census statute, there can be reasonable differences among politicians and among statisticians about the operational feasibility of the sampling design recommended by the bureau. But no statistician can accept the widespread misrepresentation of modern sampling methods. There can be no national statistics on unemployment, housing, transportation, health, or education without sampling. We can accommodate the Court ruling that Census 2000 is not to include statistical adjustment for the apportionment count, but without sampling the Census Bureau cannot fulfill its broad statistical responsibilities to policy-making, to business planning, and to scientific research. Also at issue is the damaging and unfounded claim that the bureau opted for sampling so it could then manipulate numbers for partisan purposes. To seek tactical advantage in a political dispute by questioning the integrity of a scientific agency is troubling. When national leaders say that the bureau cannot be trusted, they invite public doubt about other statistics, such as the consumer price index, poverty trends, unemployment rates, even measures of gross domestic product. When partisanship intrudes into the conduct of science, when widely accepted scientific methods are deliberately misrepresented, when scientific agencies are casually accused of dishonesty, a shadow falls across all of U.S. science.

Dynamic Stability of Imperfect Frames under Joint Displacements

In this investigation a nonlinear dynamic‐stability analysis is performed on a two‐bar geometrically imperfect frame subjected to an axial displacement of its joint, either suddenly applied or time dependent. The dynamic response of the frame is governed by a coupled system of two one‐dimensional partial differential equations for the axial and lateral motion of each bar. One and two‐mode solutions are thoroughly discussed for various geometric configurations of the frame. Dynamic buckling occurs when the corresponding frame under static loading loses its stability through a limit point. This happens for initial bar curvatures above a certain critical value; below this value the frame is dynamically stable. Numerical results are obtained by using Galerkin's method in connection with the seventh‐order Runge‐Kutta‐Verner scheme with appropriate step size. The results of the one‐mode solution are found to be in excellent agreement with those of previous analyses.

Nonsampling Error in Surveys.

Sources of Survey Error Frames: Definitions of Frames and Frame Errors Frames: Quantifying Frame Errors Frames: Conducting Surveys with Imperfect Frames Nonresponse: Background and Terminology Nonresponse: Statistical Effects of the Problem Nonresponse: Dealing with the Problem Measurement: Survey Measurement and Measurement Error Measurement: Quantifying Measurement Error Measurement: Quantifying Measurement Error, Variability in Measurement Total Survey Design: More General Error Models Compedium of Nonsampling Error Terminology.

Buckling failure probability of imperfect elastic frames

Probabilistic buckling failure of random imperfect frames is studied via the stochastic finite element method. The statistics of buckling strengths of elastic frames with random initial imperfections, uncertain sectional and material properties are inferred from the statistics of the basic system parameters through the utilization of the stochastic finite element method. The effects of variations in geometric imperfections, sectional and material properties on variation in buckling strength are investigated. The failure probability of imperfect frames consisting of random system parameters subject to random loads is computed in load space. Factors affecting the reliability of the frames are identified and discussed. It was found that sectional properties, the shape of geometric imperfection, and the magnitude of imperfection may have important effects on frame reliability.

Buckling analysis of imperfect frames using a stochastic finite element method

A stochastic finite element method is developed for the buckling analysis of frames with random initial imperfections, uncertain sectional and material properties. The random geometrical imperfections of the frames are described by member initial crookednesses which are modeled as given initial displacement functions with amplitudes treated as random variables. The effects of the random initial geometric imperfections are formulated as a set of equivalent random nodal coordinates in the finite element discretization of the members. The mean-centered second-order perturbation technique is used to formulate the stochastic finite element method for the buckling analysis of the imperfect frames. Use of the present method is illustrated by several examples of buckling analysis of random frames. Results derived from the Monte Carlo method are also obtained for comparison.

METHOD OF ESTIMATION FOR SAMPLING FROM INCOMPLETE FRAMES

SummaryThe planning of any sample survey or census requires the existence of a sampling frame comprising a list of all the sampling units. But unfortunately there is hardly a situation in practice where the frame is available in the form the sampler desires to use. Most commonly some units of the target population are not listed in the frame, and the frame may contain units which do not belong to the target population. In this investigation a suitable method of estimation is proposed when sampling is done from such imperfect frames and a geographical ordering of the units can be established.

Buckling and Postbuckling of a Symmetrically Loaded Three-Hinged Portal Frame

ABSTRACT ABSTRACT A nonlinear stability analysis based on a variational approach is performed on a symmetric three-hinged rectangular frame symmetrically loaded. The loading consists of two vertical concentrated forces which may be applied eccentrically with respect to the center lines of the columns. By using a perturbation technique the critical loads of the perfect frame corresponding to its first two buckling modes associated with bifurcational instability are established. It is also found that the sway-buckling mode either of the perfect or the imperfect frame is associated with a stable bifurcation point. The effects of loading eccentricity and slenderness ratio upon the critical load are assessed.

Large Deformation Analysis of Submerged Ring Frames

Numerical studies are reported of the response to in-plane radial loading of a series of closed ring frames of constant perimeter. Accurate second-order elastic analyses were made using a discrete element technique that has confirmed the classical buckling pressures for round cylinders under hydraulic loading. Higher buckling modes are readily predicted as well but of more significance is the demonstration of the nature of the post-buckling behavior of perfect and imperfect ring frames under uniform and nonuniform hydraulic loading of the follower type.

On the Bias in Estimation Due to Imperfect Frame in the Canadian Waterfowl Surveys

On the Bias in Estimation Due to Imperfect Frame in the Canadian Waterfowl Surveys