# Parameter Identification of Structures with Different Connections Using Static Responses
###### Abstract  
This paper presents a parameter-identification method for rod structures with different connections. In this method, the parameters of the structure are adjusted to match its analytical and measured displacements. The damage identification for truss structure and rigid frame were investigated. Previous studies often considered the cross-sectional area damage or joint damage; there are few studies on the simultaneous existence of these two types of damage. In this study, damage identification for a rigid frame with both cross-sectional and joint damage was performed. Based on the measured displacements, the proposed method can accurately identify the cross-sectional and joint damage for a rigid frame.  
parameter identification  
In practical engineering construction, several joints in frame structures are of semi-rigid connection type owing to the design or damage; the characteristics of semi-rigid connections lie fall in between those of pin and rigid connections. Notably, some studies on structures with semi-rigid connections have been conducted [12; 13; 14; 15; 16; 17]. [PERSON] and [PERSON] [12] evaluated and analyzed the nonlinear seismic response of steel structures with semi-rigid and composite connections in terms of maximum interstory and maximum top lateral displacements. [PERSON] et al. [13] carried out a numerical study on the reliability of 3D steel structures with perfectly pinned connections and semi-rigid connections under seismic loads. [PERSON] et al. [14] studied seismic performance of steel moment-resisting frames with different degrees of moment connection rigidities.  
Several methods have been presented to identify joint damage for frame structures and to reduce the error during model updating by varying the rigidity of the element connections. [PERSON] et al. [18] proposed an approach to identify the joint damage in steel frame structures using dynamic and static measurement data. [PERSON] et al. [19] presented a method for updating the finite-element model of an arch-type steel-laboratory bridge model with semi-rigid connections. [PERSON] et al. [20] presented a novel two-stage improved radial basis function neural network technique to identify the joint damage of a semi-rigid frame structure in frequency and time domains. [PERSON] et al. [21] proposed a joint damage identification method based on modal parameters using a unified particle swarm optimization method to identify joint damages in any frame structure. [PERSON] et al. [22] presented a joint damage identification technique using the numerical model of a semi-rigid frame to quantify the level of loosening of bolted joints in a steel frame structure, based on vibrations. [PERSON] et al. [23] introduced a two-step method for joint damage identification for steel frames using a support vector machine and a differential evolution algorithm. [PERSON] et al. [24] proposed a two-step damage-detection method for space-frame structures with semi-rigid connections. Numerous studies have identified cross-sectional damage in trusses and rigid frames. In addition, in some studies, joint damage was identified for semi-rigid frame structures on the basis of static and modal data. However, there are few studies utilizing static measurements for damage identification in rigid frame structures having both cross-sectional and joint damage. Therefore, this paper presents a new method to identify the damage in frame structures with both cross-sectional and joint damage.