Nonparametric estimation of a quantile qm(X),α of a random variable m(X) is considered, where m : ℝd → ℝ is a function, which is costly to compute and X is an ℝd-valued random variable with known distribution. Monte Carlo surrogate quantile estimates are considered, where in a first step, the function m is estimated by some estimate (surrogate) mn, and then, the quantile qm(X),α is estimated by a Monte Carlo estimate of the quantile qmn(X),α. A general error bound on the error of this quantile estimate is derived, which depends on the local error of the function estimate mn, and the rates of convergence of the corresponding Monte Carlo surrogate quantile estimates are analyzed for two different function estimates. The finite sample size behavior of the estimates is investigated in simulations
Abstract. Buckling of load-carrying column structures is an important design constraint in light-weight structures as it may result in the collapse of an entire structure. When a column is loaded by an axial compressive load equal to its individual critical buckling load, a critically stable equilibrium occurs. When loaded above its critical buckling load, the passive column may buckle. If the actual loading during usage is not fully known, stability becomes highly uncertain.This paper presents an approach to control uncertainty in a slender flat column structure critical to buckling by actively stabilising the structure. The active stabilisation is based on controlling the first buckling mode by controlled counteracting lateral forces. This results in a bearable axial compressive load which can be theoretically almost three times higher than the actual critical buckling load of the considered system. Finally, the sensitivity of the presented system will be discussed for the design of an appropriate controller for stabilising the active column.
Buckling of load-carrying column structures is an important failure scenario in light-weight structures as it may result in the collapse of the entire structure. If the actual loading is unknown, stability becomes uncertain. To investigate uncertainty, a critically loaded beam-column, subject to buckling, clamped at the base and pinned at the upper end is considered, since it is highly sensitive to small changes in loading. To control the uncertainty of failure due to buckling, active forces are applied with two piezoelectric stack actuators arranged in opposing directions near the beam-column’s base to prevent it from buckling. In this paper, active buckling control is investigated experimentally. A mathematical model of the beam-column is built and a model based Linear Quadratic Regulator (LQR) is designed to stabilize the system. The controller is implemented on the experimental test setup and a statistically relevant number of experiments is conducted to prove the effect of active stabilization. It is found that the load bearing capacity of the beam-column could be increased by more than 40% for the experimental test setup using different controller parameters for three ranges of axial loading
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