Framework for Comparison Study of Stochastic Modal Identification Considering Accuracy and Efficiency

This paper presents a framework to compare the performance of the system identification methods by investigating the accuracy of the identified results and efficiency of the methods represented by computational costs. The successful identification reproduces the given structural system using accurate modal parameters with minimizing noise effect with the least computational cost. The accuracy of the algorithm is estimated through the distribution of identified modal parameters corresponding to the size of the transition state matrix instead of calculating errors compared to the exact values due to the insufficient information about modal parameters in a physical structure. Three modal parameters, vibration frequencies, damping ratios, and mode shapes, equally contribute to quantify the accuracy of the algorithm. As a measure of efficiency, two computational cost measures, number of operations and computational time in a single loop of each algorithm, are considered together to complement each other. Application of the framework for comparison study is performed for the acceleration data from the Riverton-Belvidere Bridge over the Delaware River. A Wireless Sensor Network (WSN) is implemented to acquire the response of the bridge due to ambient excitations. A total of eight sensor nodes are installed on the main span of the bridge, measuring the vertical and transverse accelerations. Based on the deployment of sensors, four sensors on each side, the system identification of the bridge is possible for vertical, torsional, and transverse modes. Four stochastic modal identification methods, including Eigensystem Realization Algorithm (ERA)-Observer Kalman Filter Identification (OKID), ERA-Natural Excitation Technique (NExT), ERA-NExT-AVG, and Auto-Regressive (AR) models, are used to identify modal parameters of the bridge and examine the identified results. The estimates of structural modes for frequencies are up to 20 Hz for all investigated methods. The comparison study shows that the proposed framework is effective to estimate the performance of system identification method.