Identification of Inelastic Shear Frames Using the Prandtl-Ishlinskii Model

Abstract. In this paper, a new method is proposed for identi cation of inelastic shear frame structures with hesteresis, using data collected on their dynamic response. It uses the Prandtl-Ishlinskii rate independent model for hysteresis, which was originally used in the eld of plasticity and ferromagnetism. The proposed identi cation method is capable of identifying the mass, damping and restoring force of a frame structure, which can be used in forming the equations of motion of the frame. By solving the equations of motion, the dynamic response is predicted. The method is based on the combined use of Quadratic Programming (QP) and Genetic Algorithms (GA). First, assuming a set of Prandtl-Ishlinskii constants, the QP is used to nd the best frame parameters that can be used in its equations of motion to predict its dynamic response with the minimum of error compared to the real data collected on its dynamic response, while the GA is used to nd the best Prandtl-Ishlinskii constants for more reduction in error. The method has been applied to di erent frames with bilinear nonlinearity where the results show the high capability of the method. Two examples, a Single and a Multi Degree Of Freedom (SDOF and MDOF) frame, are included in the paper. Keywords: Prandtl-Ishlinskii model; Identi cation; Inelastic behavior; Structural dynamic; Earthquake.