State-space system identification with physically motivated residual states and throughput rank constraint

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It has been observed that energy conjugate input-output pair transfer functions with strongly participating outside-band modes of mechanical systems often render identified state-space models with poor fit to data. That holds even after common practice inclusion of mass and stiffness residual states. The inclusion of a particular form of extra residual states are suggested to improve the model fit for such pairs. A pole placement strategy for the extra states is derived. Furthermore, for identification of state-space models with force input and acceleration output, the system direct throughput matrix relating the two is modelled. For flexible structures with rigid body motion, it is shown that the direct throughput matrix can be decomposed into a rigid body and flexible motion part. In test situations with more inputs and outputs than rigid body modes, the rigid body partition of the direct throughput matrix of the identified model must be rank constrained for physical consistency. The constraint is enforced using a singular value decomposition during iterations of the state-space matrices used to further improve the identified model fit. The procedures are illustrated on simulated finite element data from an industrial component with known model order. A successful application to real experimental data is also shown.