Novel computation method of reducing ill-posedness for structural static distributed load identification by optimising strain gauge locations

Abstract

The static distributed load exerted on engineering structures, such as the ice extrusion load on steel gates or stop logs in cold regions, is sometimes difficult to measure directly. However, load identification provides an effective approach of indirect load monitoring. Load identification is an inverse problem in structural mechanics, and the mathematical model used for load identification is typically ill-posed. This ill-posedness results in certain difficulties in the inverse calculation and decreases the precision of load identification. In this study, the condition number of the transfer matrix of the mathematical model used for load identification, called C-optimal design (COD), was employed as the objective function to overcome the ill-posedness by optimising the strain gauge locations. A successive reduction algorithm (SRA) was developed to perform the COD directly. On this basis, a block C-optimal design (BCOD) was further developed to reduce computational cost. The COD with SRA and BCOD were described in detail through a specific case study, i.e., a steel gate in a cold region, in which the mathematical model was established by dividing the ice load monitoring zone into several individual cells and assuming that the ice load exerted on every cell is equivalent and uniform. Several numerical examples were used to verify the effectiveness of BCOD. The simulation results of load identification demonstrate that the BCOD method is more beneficial for obtaining stable and accurate identification results than a D-optimal design (DOD) method. Moreover, an experiment was designed and performed to further verify the advantage of BCOD. The experimental results indicate that the BCOD can provide more accurate identification results than the DOD; these results are approximately consistent with the simulation results.