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This paper discusses an algorithm lo compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identificatinn of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Huhhle space telescope.

This paper discusses an algorithm lo compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identificatinn of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Huhhle space telescope.

SUMMARYIn this paper, an adaptive on-line parametric identiÿcation algorithm based on the variable trace approach is presented for the identiÿcation of non-linear hysteretic structures. At each time step, this recursive least-square-based algorithm upgrades the diagonal elements of the adaptation gain matrix by comparing the values of estimated parameters between two consecutive time steps. Such an approach will enforce a smooth convergence of the parameter values, a fast tracking of the parameter changes and will remain adaptive as time progresses. The e ectiveness and e ciency of the proposed algorithm is shown by considering the e ects of excitation amplitude, of the measurement units, of larger sampling time interval and of measurement noise. The cases of exact-, under-, over-parameterization of the structural model have been analysed. The proposed algorithm is also quite e ective in identifying time-varying structural parameters to simulate cumulative damage in structural systems.

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In this study a new solution for the identification of physical parameters of mechanical systems from identified state space formulations is presented. With the proposed approach, the restriction of having a full set of sensors or a full set of actuators for a complete identification is relaxed, and it is shown that a solution can be achieved by utilizing mixed types of information. The methodology is validated through numerical examples, and conceptual comparisons of the proposed methodology with previously presented approaches are also discussed.

This work tackles the problem of global identifiability of an undamped, shear-type, N degrees of freedom linear structural system under forced excitation without any prior knowledge of its mass or stiffness distributions. Three actuator/sensor schemes are presented, which guarantee the existence of only one solution for the mass and stiffness identification problem while requiring a minimum amount of instrumentation (only 1 actuator and 1 or 2 sensors). Through a counterexample for a 3DOF system it is also shown that fewer measurements than those suggested result invariably in non-unique solutions.