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We examine the sensitivity of noisy time series of data from a chaotic system to changes in the parameters of the system. The investigation yields two insights: (1) A small fraction of the data contains most of the information about the parameters. (2) For one-parameter families of systems, there is often a preferred direction in parameter space governing how easily trajectories of nearby systems shadow each other. A parameter estimation algorithm is presented that leverages these properties of chaotic systems to yield estimate errors that decrease as ${1/N}^{2}$, where $N$ is the number of state samples used.

In this paper experiments on the quasistatic and dynamic behaviour of the electrostatic polysilicon microrelay fabricated at IMT are presented together with new nonlinear dynamical models. The models simulate the pull-in voltage, the resonance frequency, the quality factor, the switching time and the electrostatic spring softening of the microrelay. Simulation of the pull-in voltage has been done with MIT's MEMCAD system, the resonance frequency has been simulated with Abaqus/sup TM/, while macro-models developed at MIT have been used to simulate the dynamics of the nonlinear actuator in the presence of squeeze-film damping.

In this paper, are describe how a few simulations of fully meshed dynamical problems can be used to construct efficient low-order models for system-level design of microstructures. We report on the use of this method to capture the measured behaviour of a pressure sensor based on the pull-in time of a beam. Results show that the reduced order model decreases simulation time by at least a factor of 37 while achieving good agreement with experimental data.