Long-term observations of the Antarctic ice sheet will contribute to a quantitative evaluation and precise prediction of the sea level change induced by global changes in climate. This paper proposes an improved rigorous geometric modeling method for the declassified <small>KH-5
ARGON</small> satellite images collected in Antarctica in 1960s. The scanned film images are preprocessed beforehand to enhance the quality for further analysis. Systematic errors such as lens distortion and atmospheric refraction are also considered and corrected. A scheme is proposed
to measure the ground control points for the historical images based on modern image mosaic and <small>DEM</small> products. The bundle adjustment results of four blocks in regions in East Antarctica present a geometric positioning accuracy of less than one nominal pixel resolution
(140 m) in both horizontal and vertical directions, outperforming the published results. A regional <small>DEM</small> of the ice sheet that represents the topography in 1963 is then generated from the stereo <small>ARGON</small> images for the first time, the evaluation
of which shows its consistency with the modern product but with great value for studying the recent change history of the ice sheet.
A formulation of statistical linearization for multi-degree-of-freedom (M-D-O-F) systems subject to combined mono-frequency periodic and stochastic excitations is presented. The proposed technique is based on coupling the statistical linearization and the harmonic balance concepts. The steady-state system response is expressed as the sum of a periodic (deterministic) component and of a zero-mean stochastic component. Next, the equation of motion leads to a nonlinear vector stochastic ordinary differential equation (ODE) for the zero-mean component of the response. The nonlinear term contains both the zero-mean component and the periodic component, and they are further equivalent to linear elements. Furthermore, due to the presence of the periodic component, these linear elements are approximated by averaging over one period of the excitation. This procedure leads to an equivalent system whose elements depend both on the statistical moments of the zero-mean stochastic component and on the amplitudes of the periodic component of the response. Next, input–output random vibration analysis leads to a set of nonlinear equations involving the preceded amplitudes and statistical moments. This set of equations is supplemented by another set of equations derived by ensuring, in a harmonic balance sense, that the equation of motion of the M-D-O-F system is satisfied after ensemble averaging. Numerical examples of a 2-D-O-F nonlinear system are considered to demonstrate the reliability of the proposed technique by juxtaposing the semi-analytical results with pertinent Monte Carlo simulation data.
A statistical linearization approach is proposed for determining the response of the single-degree-of-freedom of the classical Bouc-Wen hysteretic system subjected to excitation both with harmonic and stochastic components. The method is based on representing the system response as a combination of a harmonic and of a zero-mean stochastic component. Specifically, first, the equation of motion is decomposed into a set of two coupled non-linear differential equations in terms of the unknown deterministic, and stochastic response components. Next, the harmonic balance method, and the statistical linearization method are used for the determination of the Fourier coefficients of the deterministic component, and the variance of the stochastic component, respectively. This yields a set of coupled algebraic equations which can be solved by any of the standard apropos algorithms. Pertinent numerical examples demonstrate the applicability, and reliability of the proposed method.
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