Identification of dynamic systems using Multiple Input–Single Output (MISO) models

Abstract

System identification is a method used to obtain the modal characteristics of existing structural systems through dynamic observations. Modal characteristics of the system can be used for a variety of purposes, including model updates, damage assessment, active control and original design re-evaluation. In this paper, the transfer functions relating the input quantities (traffic load, wind speed and temperature variations) and output quantities (lateral and longitudinal movement) of the towers of the Bosphorus Suspension Bridge were defined with the help of two models, namely, the parametric Multiple Input–Single Output (MISO) Auto-Regressive with eXogenous input (ARX) and the multiple regression models. The latter model was primarily used to check for the existence of outlier measurement(s) and to identify the input quantities that have a significant contribution to the structural movements since outlier measurements in observations and insignificant input quantities increases the difficulty of defining the parameters of the inherently complex MISO ARX model. Least Squares (LS) and bi-square weighted robust predictors were used to determine the parameters of the multiple regression model used in this study. Regression analysis showed that there were no outlier measurements in the tower observations and the effect of wind speed on the longitudinal movements was statistically insignificant. Furthermore, the sensitivity of LS and bi-square robust predictors to outlier measurements were also checked in the regression analysis by adding rough errors to the observations. Finally, it was also observed that the MISO ARX512, ARX511, ARX411 and ARX415 models defined by taking into account the results of regression analysis estimate structural movements more accurately than the multiple regression model ARX010.