92 S. W. B. Klaassen and D. J. Rixen YPar YOv YRem YSEMM Fig. 10.4 The parent model and overlay model are coupled. The parent model Ypar contains all the DoF required but contains an erroneous joint. The overlay model Yov is a set of measurements of the system with the correct joint, but lacks the DoF required to identify this joint. From this, the removed model—in this case a copy of the parent model—is decoupled. The resulting SEMM model YSEMM has the correct joint (from the overlay model) and also has the required DoF to decouple (from the parent model) System Equivalent Model Mixing (SEMM) is a method that uses substructuring to expand model dynamics contained in an overlaymodel Yov onto the DoF-space of aparent model Ypar. In Fig. 10.4 the process is drawn schematically for component AB. Let us start by stating the equation of motion for the SEMM-system which directly follows from the schematic in Fig.10.4. u =Y(f −g), with Y= ⎡ ⎣ Ypar −Yrem Yov ⎤ ⎦ , f = ⎡ ⎣ fpar frem fov ⎤ ⎦ , g = ⎡ ⎣ gpar grem gov ⎤ ⎦ (10.18) Here, the models Ypar , Yrem , Yov are the so-called parent, removed, and overlay models respectively. These are the building blocks for SEMM; they are derived below. In order to apply the method in the joint-identification case we require: 1. FRF-based component models that contain the entire DoF-set including boundary DoF. These may be either numerical or experimental in nature (note: it may be possible to measure the boundary DoF in the unassembled state). 2. A set of measurements of an assembled full-system that observe the joint dynamics but do not have explicit boundary DoF. Requirement one is the parent model: To compute the parent model the component models can either be left uncoupled (in block-diagonal form) or coupled with an initial guess joint model: Ypar = YAB gg = ⎡ ⎢⎢ ⎢⎣ YAB iAiA YAB iAiB YAB iAbA YAB iAbB YAB iBiA YAB iBiB YAB iBbA YAB iBbB YAB bAiA YAB bAiB YAB bAbA YAB bAbB YAB bBiA YAB bBiB YAB bBbA YAB bBbB ⎤ ⎥⎥ ⎥⎦ (10.19) where the (global) DoF-set g contains the boundary DoF-set b (c.f. the red markers in Fig. 10.4) and the internal DoF-set i (c.f. the black markers in Fig. 10.4) such that g =col iA iB bA bB are all the DoF of component AB. Note that if the joint is in fact rigid, then due to the compatibility equation (10.5) the third and fourth row, and third and fourth column are redundant since DoFbA =bB. It is important that the parent model, as postulated above, contains a flexible initial guess joint such that DoF bA =bB for reasons which will be explained later. Note that an uncoupled model (infinitely flexible joint) is then also permitted. In this specific case the cross-terms between the components are all zero. Next, the full-system measurements (which observe the joint dynamics) are required. These become the so-called overlay model: Yov = YAJB iAiA YAJB iAiB YAJB iBiA YAJB iBiB (10.20) As stated before, the measurements can only be done for the internal DoFiA, iB.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==