Experimental Evaluation of Drive-by Health Monitoring on a Short-Span Bridge Using OMA Techniques 111 Fig. 1 Example demonstrating the difference between the loosely coupled system model traditionally assumed under for OMA and the strongly coupled system model used in DBHM. (a) Conventional loosely coupled system; (b) strongly coupled vehicle-bridge system for DBHM He(ω) = Oe(ω) G(ω) , (2) Hs(ω) = Os(ω) Oe(ω) , (3) where G(ω), Oe(ω), and Os(ω) represent the Fourier transformations of the assumed Gaussian noise input to the excitation system, the output from the excitation system, and the subject structure’s output, respectively [1]. As the output from the structure represents the output response of the coupled system, it contains modal information from both subsystems. Under the traditional SHM paradigm, vehicle-bridge systems closely resemble the framework outlined in Eqs. (1)–(3) and Fig. 1a, where vehicles serve as the excitation system and the bridge response serves as the output of the entire system [1, 23]. Under the DBHM paradigm, however, vehicle-bridge systems create a strongly coupled system where the output from the bridge system feeds back into the vehicle system and the vehicle’s response is treated as the entire system’s output, as seen in Fig. 1b. A number of different criteria may apply when classifying OMA techniques, with each criterion highlighting specific benefits and shortcomings common to different techniques in order to guide researchers towards the most appropriate analysis procedures for a given framework. Figure 2 provides a visual breakdown of the classifications for OMA system identification techniques, while information pertaining to the benefits and pitfalls of the classifications can be obtained from [1, 2]. In this study, nonparametric single degree-of-freedom (SDOF) frequency domain techniques are utilized to evaluate the feasibility of employing OMA towards DBHM data. Nonparametric SDOF techniques are selected for this initial study because of their computational efficiency and the presence of a dominant fundamental frequency in most bridge systems [1]; however, future work will include the examination of parametric techniques that can achieve greater predictive accuracy. Section 2.1 provides a brief overview of the OMA techniques examined in this research, while Sect. 2.2 addresses the implementation of the techniques in DBHM. 2.1 Frequency Domain OMA Techniques The simplest nonparametric OMA technique to implement in the frequency domain is PP. The technique is classified as a SDOF approach due to the assumption that only one mode is present around resonant peaks [2]. PP works by first calculating the power spectral density (PSD) of a system’s outputs and then identifying resonant frequencies as the extreme values within the spectrum. The technique can also be leveraged to identify operational deflection shapes and system damping. Despite being simple and intuitive to use, the PP technique is only effective when system damping is low and modes are well separated; however, it is still a useful technique for obtaining initial system identification results in a fast and computationally inexpensive manner [1, 2]. FDD is similar to PP in the sense that modal parameters are estimated from peak frequencies within a subject response spectrum. FDD improves on the PP technique, by leveraging singular value decomposition (SVD) to decompose the cross power spectral density (CPSD) matrix into sets of SDOF systems, thus enabling the detection of closely spaced modes [1, 24]. The detection of closely spaced modes is exact for cases where fundamental OMA assumptions are met, the structure is lightly damped, and the closely spaced mode shapes are geometrically orthogonal; this holds true even under a high level
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