A Framework for the Use of Mobile Sensor Networks in System Identification

System identification (SID, also known as structural identification in this context) is the process of extracting a system’s modal properties from sensor measurements. Typically, a mathematical model is chosen for data fitting and the identification of model parameters yields modal property estimates. Historically, SID has relied on measurements from fixed sensors, which remain at specific locations throughout data collection. The ultimate flaw in fixed sensors is they provide restricted spatial information, which can be addressed by mobile sensors. In this dissertation, a framework is developed for extracting structural modal estimates from data collected by mobile sensors. The current state of mobile sensor networks applications in SHM is developing; research has been diverse, however limited. Reduced setup requirements for mobile sensor networks facilitate data collection, thus enable expedited information updates on a structure’s health and improved emergency response times to natural disasters. This research focuses on using mobile sensor data, i.e., data from sensors simultaneously recording in time, while moving in space, for comprehensive system identification of real structural systems. Mobile sensing data is analyzed from two perspectives, each requires different modeling techniques: an incomplete data perspective and a complete data perspective. In Chapter 2, Structural Identification using Expectation Maximization (STRIDE) is introduced, a novel application of the Expectation Maximization (EM) algorithm and approach for output-only modal identification. Chapter 3 revisits STRIDE for consideration of incomplete datasets, i.e., data matrices containing missing entries. 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, e.g., mobile sensing. It is demonstrated that sensor network data containing a significant amount of missing observations can be used to achieve a comprehensive modal identification. Moreover, a successful real-world identification with simulated mobile sensors quantifies the preservation of spatial information, establishing benefits of this type of network, and emphasizing an inquiry for future SHM implementations. In Maximum Likelihood (ML) estimation theory, on which STRIDE is based, the precision of ML point estimates can be measured by the curvature of the likelihood function. Chapter 4 presents closed-form partial derivatives, observed information, and variance expressions for discrete-time stochastic state-space model entities. Confidence intervals are constructed for natural frequencies, damping ratios, and mode shapes using the asymptotic normality property of ML estimators. In anticipation of high-resolution scanning, mobile sensor data is also perceived to belong to a general class of data called dynamic sensor networks (DSNs), which inherently contain spatial discontinuities. Chapter 5 introduces state-space approaches for processing data from sensor networks with time-variant configurations for which a novel truncated physical model (TPM) is proposed. In typical state-space frameworks, a spatially dense observation space on the physical structure dictates a large state variable space, i.e., more total sensing nodes require a more complex dynamic model. The result is an overly complex dynamic model for the structural system. As sensor networks evolve and with increased use of novel sensing techniques in practice, it is desirable to decouple the size of the structural dynamic system from spatial sampling resolution during instrumentation. The TPM is presented as a novel technique to reduce physical state sizes and permit a general class of DSN data, with an emphasis on mobile sensing. Also, the role of basis functions in the approximation of mode shape regression is established. Chapter 6 discusses the identification of the TPM using an adjusted STRIDE methodology

On parameter estimation using nonparametric noise models

Fitting multidimensional parametric models in frequency domain using nonparametric noise models is considered in this paper. A nonparametric estimate of the noise statistics is obtained from a finite number of independent data sets. The estimated noise model is then substituted for the the true noise covariance matrix in the maximum likelihood loss function to obtain suboptimal parameter estimates. The goal here is to present an analysis of the resulting estimates. Sufficient conditions for consistency are derived, and an asymptotic accuracy analysis is carried out. The first- and second-order statistics of the cost function at the global minimum point are also explored, which can be used for model validation. The analytical findings are validated using numerical simulation results