Solving Inverse Problems in Structural Damage Identification

Accurately identifying damage is difficult after an extreme event since damage often cannot be directly measured. Sensors, however, can collect data that reflects damage by measuring changes in structural response. Therefore, damage identification becomes an inverse problem in which the goal is to find system properties using limited response information. The inverse problem is formulated as an optimization problem and is solved using an implicit redundant representation genetic algorithm (IRR GA). Element damage is introduced into the finite element model using a damage indicator to represent a loss of stiffness. The set of damage indicators are optimized by minimizing the difference between frequency response functions obtained from the damaged structure and the updated structural model. Although an accurate structural model may require thousands of finite elements, the number of damaged elements is typically much smaller. The problem, however, is that the number of damaged elements and their locations are not known beforehand, which leads to an unstructured optimization problem. To solve this problem the IRR GA uses redundant segments to allow the number of design variables (damage indicators) to change during optimization. A damage scenario can then be represented by only a small subset of damage indicators, instead of all possible damaged elements. The performance of the method on two-span beam and multi-story frame structures was evaluated using several imposed damage scenarios. High damage identification accuracy was obtained with limited sensor data even when measurement noise was present in the sensor data. The method also was able to identify damage in larger systems that are difficult to solve using existing methods due to the large number of design variables.