Comparing Model Update Error Residuals and Effects on Model Predictive Accuracy

Abstract

The effect of error residual choice on the predictive capability of an updated structural model is examined. First, analytical expressions are developed that relate errors in dynamically measured static flexibility matrices, stiffness matrices, and modal matrices. The analysis shows that flexibility, stiffness, and modal error residuals correspond to unique weightings on the error in the measured modal data. Next, the flexibility weighting indicator and the stiffness weighting indicator are defined to provide a simple means of ranking individual modes in terms of their potential contribution to errors in a measured static flexibility or stiffness matrix. Finally, expressions are developed for bounding model prediction errors when static flexibility, stiffness, or modal error residuals are used. The results show that the amount of uncertainty in predicted static displacements, static loads, and mode shapes and frequencies is directly related to the choice of error residual and is different in each case. These results are also illustrated using numerical simulations for a modified version of Kabe's problem, which includes model form errors.