9. The Application of a Force Identification Method Based on Particle Swarm Optimization to Compression Steel Bars

The non-destructive determination of internal forces in bars for existing building structures is a forward-looking challenge for the construction industry. The application of validated techniques would not only allow the detection of overloads or structural changes according to the load-bearing behavior, it would also allow the verification of the original structural analysis. Based on an experimental modal analysis, tried and tested methods to determine the tensile forces of cables in the operating condition have existed for many years. Due to the slenderness of the cables, even normal forces have a large influence on their natural frequencies: The higher the tensile forces, the higher the geometrical system stiffness, which increases natural frequencies. An equivalent effect occurs when considering load-bearing elements subjected to compression, whereby larger compressive forces lead to a reduction in the geometrical system stiffness and thereby to a reduction in natural frequencies. While various methods have been experimentally investigated for tension cables and tension rods, only a few elaborations are known with respect to structural compression rods. This research presents a system identification method based on the experimental determination of the modal parameters of a compression steel bar. Using an iterative optimization procedure, the design parameters of a basic model including the compressive force are iteratively adjusted until the best possible agreement between the experimental measurements and a theoretical analysis is found. For this purpose, a deviation function is formulated and an evolutional algorithm — in this case facilitating a Particle Swarm Optimization — is used to solve the optimization problem. The Particle Swarm Optimization is an innovative metaheuristic algorithm that allows searching for the global minimum even for complicated nonlinear functions. The method is experimentally validated on slender steel beams with varying compressive forces. Laboratory results from three different steel profiles combined with two different bearing conditions each are presented. Therefore, six specimens were constructed and tested with four different force levels each. The average deviation over all 24 tests between the optimized force and the actual force directly measured by a load cell was determined as 7.4%.