Lagrange multiplier state-space substructuring

In this article a new state-space coupling formulation, named Lagrange Multiplier State-Space Substructuring (LM-SSS), is presented. This method represents an evolution of the classical state-space substructuring method (classical SSS). Likewise the well-known Lagrange Multiplier Frequency Based Substructuring (LM FBS) method, the LM-SSS is achieved by using a dual assembly formulation, which means that the full set of degrees of freedom (DOFs) is retained. The equilibrium and compatibility conditions are established by directly considering the connecting forces. The LM-SSS method has demonstrated to be simple to understand and to implement in a computational environment. Furthermore, since the formulation uses a mapping matrix to enforce the coupling conditions, several substructures can be coupled at same time. Similar to classical SSS, this method is not able to directly compute a minimal-order coupled state-space model. However, two post-processing procedures are presented in order to compute a minimal realization of the obtained coupled state-space models by using these techniques. By coupling numerical data is found that when dealing with state-space models estimated from noise-free data the same solutions are obtained by using the classical SSS or the LM-SSS. However, by comparing both methods is clear that the LM-SSS may have advantages over the classical method when dealing with state-space models estimated from experimental data, since it requires the inversion of only one matrix, thus reducing the instability of the associated numerical problems.