Structural Identification for Mobile Sensing with Missing Observations

There are many occasions in structural health monitoring (SHM) on which collected data sets contain missing observations. Such instances may occur as a result of failed communications or packet losses in a wireless sensor network or as a result of sensing and sampling methods—for example, mobile sensing. By implementing modified expectation and maximization steps, structural identification using expectation maximization (STRIDE) is capable of processing data in these circumstances and is the first modal identification technique to formally accept data with missing observations. This paper presents the STRIDE algorithm, a statistical perspective of missing data, and new STRIDE equations that account for missing observations. Expectation step (E-step) equations are given explicitly for both partially observed time steps and those not fully observed. The maximization step (M-step) provides state-space parameter updates in terms of available observations and missing-data state-variable statistics. This paper also discusses the performance and convergence behavior of STRIDE with missing data. Finally, two applications are presented to exemplify common use in network reliability and mobile sensing, both using data collected at the Golden Gate Bridge. This paper proves that sensor network data containing a significant amount of missing observations can be used to achieve a comprehensive modal identification. A successful real-world identification with simulated mobile sensors quantifies the preservation of spatial information, establishing the benefits of this type of network and emphasizing a line of inquiry for future SHM implementations.