Derivation of a new parametric impulse response matrix utilized for nodal wind load identification by response measurement

This paper provides new formulations to derive the impulse response matrix, which is then used in the problem of load identification with application to wind induced vibration. The applied loads are inversely identified based on the measured structural responses by solving the associated discrete ill-posed problem. To this end - based on an existing parametric structural model - the impulse response functions of acceleration, velocity and displacement have been computed. Time discretization of convolution integral has been implemented according to an existing and a newly proposed procedure, which differ in the numerical integration methods. The former was evaluated based on a constant rectangular approximation of the sampled data and impulse response function in a number of steps corresponding to the sampling rate, while the latter interpolates the sampled data in an arbitrary number of sub-steps and then integrates over the sub-steps and steps. The identification procedure was implemented for a simulation example as well as an experimental laboratory case. The ill-conditioning of the impulse response matrix made it necessary to use Tikhonov regularization to recover the applied force from noise polluted measured response. The optimal regularization parameter has been obtained by L-curve and GCV method. The results of simulation represent good agreement between identified and measured force. In the experiments the identification results based on the measured displacement as well as acceleration are provided. Further it is shown that the accuracy of experimentally identified load depends on the sensitivity of measurement instruments over the different frequency ranges.