Accurate estimation of dynamic forces acting on a structure can be useful in the areas of diagnosis, control and fatigue life prediction. Direct measurements of such forces are often inconvenient or impossible to make when structure system is in operation. The vibration due to these dynamic forces is generally easier to measure, although the measured vibration responses are modified and altered by the respective transfer paths to the measurement locations. If the transfer functions between force input points and vibration measurement locations are known, then the input forces can be identified from the response measurements. It is known as a general inverse problem notorious for the ill-conditioned nature.
In this work, two approaches to solving ill-conditioned matrix problems are presented, concentrating on those problems where model inaccuracy is the major source of error. The first one is a general technique implemented for identifying multiple input forces by using multiple vibration measurements and the structure frequency response function matrix. By applying the regularization method based on singular value decomposition in the frequency domain, the uncertainties on the force estimation, which is mainly caused by potential singularities of noise contaminated transfer function matrix, can be eliminated effectively. Optimization criterion for the iterative selection of regularization constant is suggested to minimize the noise content in the estimated forces. The second one is the technique for accurately estimating multiple forces by improving the condition of frequency response function matrix. The accuracy of the estimated forces can be severely distorted not only due to improper selections of the response measurement positions but also due to the coincidence of the excitation frequency to one of the structure natural frequencies. The selection algorithm of measurement positions is suggested. The algorithm is very systematic and effective. The basic idea is to make the contribution of each mode to the response be as uniform as possible. Also the frequency components of input forces near structure natural frequencies can be easily identified by attaching a dynamic damper at a proper location. The addition of a dynamic damper greatly eases the ill-conditioned problem especially near a resonance frequency.
The suggested techniques are tested and discussed numerically using example structures and the feasibility for practical applications has been demonstrated through experiments. The test results show that the regularization technique is very useful for reducing the effects of measurement inaccuracies on the force identification, the response selection and the dynamic damper addition idea are very effective to relieve the ill-conditioned problem, especially when the structure has large degrees of freedom and when the excitations are near one of the structure natural frequencies.
