14 A Coupled Approach for Structural Damage Detection with Incomplete Measurements 151 14.5.2 Data from Undamaged Structure The issues from this step in the process include the expected measurement noise and the inevitable lack of a complete measurement set (both spatially and with respect to the critical modes of the structure). As was suggested earlier, this process appears to be fairly robust with respect to noise and the a primary reason to develop this procedure was to attack the incomplete measurement problem. 14.5.3 Reduction Transformation Matrix The lack of ability for a reduced system to reproduce the relevant aspects of the full system is a common and well-known problem. The original procedure is likely suffering from reduction errors affecting the system changes that are due to damage through the dynamic residuals and expansion steps that follow. Dealing with the reduction issues is one of the areas of near term work that should be undertaken. 14.5.4 Matrix Disassembly The matrix disassembly step proposed in the original process was a general approach that broke the stiffness matrix up into simple springs. This did retain the proper coupling in the end but could allow some non-physical stiffnesses to result. A more rigorous and potentially robust approach would be to disassemble based on the actual element coupling used in building the models. This is certainly technically viable but may be beyond the implemented state-of-the-art for many commercialscale finite element programs. A second issue at this step involves the need to down select from the huge number of potential simple springs in the disassembled matrix to the set that will be used for creating basis vectors. There is certainly the issue that damage information may be missed or incorrect, however it is technically useful to understand which parts of the structure cannot be monitored for damage given the selected measurement set. There is some additional study that is needed to derive a set of targeted metrics (as opposed to the MAC values) that will help sort the simple springs (or disassembled elements) that will be used for damage monitoring and assessment. 14.5.5 Data from Damaged Structure The issues associated with this step are the same as were already mentioned in the Data from Undamaged Structure step. 14.5.6 Dynamic Residual Expansion The issues in this step revolve around the necessary expansion of the limited measured data set to the larger unmeasured data set. Since the inability to measure every Degrees-Of-Freedom (DOFs) in the model is a physical constraint, it is unlikely that much progress can be made on these issues in the near term. However, since this step in the process is critically dependent on the reduction/expansion transformation used, there is some hope for minor near-term improvements that can be realized by improving and tailoring the transformation process used as well as selecting the basis vectors form the disassembly process. 14.5.7 Mode Shape Expansion Many of the same issues that plague the dynamic residual expansion exist in this step as well, namely the physical constraint of unmeasured DOFs. In fact the expansion of the mode shapes will be dependent on the expansion of the dynamic residuals in the previous step. Hence, improving and understanding that process is likely to be a precursor to understanding the errors in the mode shape expansion step. Additionally, there is a need to further study the effectiveness of the novel expansion technique provided in the original work.
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