Vibration Based Damage Identification in Welded Asymmetrical Steel Frames Using Regularization Techniques

Abstract

The damage identification problem for a frame structure can be formulated in a linear equation in the form Aθ = b. In this formulation, matrix A represents the FE model parameters, vector θ represents the change in state variables or the mathematical parameters which are to be determined, and vector b represents the response to an external excitation. In the real test case, the matrix A can be rectangular, and the linear relation is an over-determined and ill-posed problem. The results of these ill-posed problems are non-continuous and thus require special solution techniques like regularization techniques for getting a solution. This study is aimed at damage identification based on the vibration analysis of asymmetrical multistory plane frame structures with welded joints. Time-domain response analysis assisted by various regularization techniques is used to identify the damage in the portal frame structures, which is caused due to loss of stiffness. Initially, the effectiveness of the regularization method is examined by considering a one-story steel frame with welded connection, which is then analyzed analytically with FE formulation by simulating single damage cases. The analysis has been extended for an instrumented multistory asymmetrical plane frame structures for single damage cases with static analysis. Various regularization techniques like Lð regularization or Least absolute shrinkage and selection operator (LASSO), Lï regularization, elastic net regularization, and linear regression are used to study their effectiveness in the damage identification without doing model updating of the numerical model. In the study, the Lð regularization gives better results than other methods for a single damage case. The damage identification in asymmetrical steel frames needs to be better studied, and this study can be replicated for more complex steel structures for real-life damage scenarios. This can be developed as a real-time standalone early warning system for important steel frame structures, thus ensuring their timely maintenance and continuous sustainable use.