Displacement and Velocity Estimation in Building Structures Using an Algebraic Observer

Abstract

This study addresses the problem of estimating the velocity and displacement in building structures. Initially, the dynamics of a building subject to seismic disturbance are represented using the Euler-Bernoulli beam model. Subsequently, the model is discretized into a finite number of floors through a modal coordinate transformation that produces a set of decoupled dynamics for each story of the building. The Algebraic Observer (AO) takes advantage of this property to ensure the Algebraic Observability Conditions (AOC). This approach allows the representation of velocity and displacement terms as functions of the available acceleration measurements. One notable advantage of the proposed observer is that, due to its design, it does not require tuning of gains to achieve the convergence property. This observer's simplicity of implementation for practical purposes is another noteworthy characteristic. Note that, to minimize the effect of the measurement noise, iterated integrals of the measured acceleration are introduced to mitigate high-frequency noise. In contrast, second-order filters are employed for low-frequency noise. Finally, the experimental demonstration of the effectiveness and accuracy of this estimation method is conducted using a reduced-scale five-story building prototype.