# Automated Modal Analysis Using Stochastic Subspace Identification and Field Monitoring Data
## 1 Introduction  
Modal parameters, such as natural frequency, damping ratio, and mode shape, reflect structures' fundamental behaviors and dynamic characteristics. Hence, the accurate identification of modal parameters is essential for structural health monitoring (SHM), as it provides critical insights into the presence of damage or degradation within the structure [1,2]. Currently, two primary approaches are commonly used to identify modal parameters from structures: experimental modal analysis (EMA) and operational modal analysis (OMA). EMA involves applying known excitations, typically using mechanical shakers or impact hammers, and measuring the resulting responses with sensors, such as accelerometers [3,4]. Generally, frequency response functions obtained from these structural responses are then analyzed using techniques, such as curve fitting or system identification techniques, to extract the modal parameters. In contrast, OMA estimates modal parameterssolely from the structural responses measured in the ambient environment, without the need for controlled excitations [5; 6]. Certainly, this approach is especially advantageous for continuous and long-term SHM, and is particularly applicable to complex structures or field applications, where applying controlled excitations is difficult or impractical. In past decades, OMA has seen significant advancements, with numerous methods developed and successfully applied to civil structures. These identification techniques are broadly categorized into frequency-domain approaches and time-domain approaches [7; 8; 9]. Specifically, the first analyzes measured responses in the spectral domain and the latter directly analyzes them over time. For instance, frequency-domain approaches include peak-picking on the power spectrum, frequency-domain decomposition (FDD), enhanced FDD, Bayesian fast Fourier Transform (FFT), Bayesian spectral density, the Gaussian mixture model, and so on [10; 11]. Recently, innovations in signal processing and system identification techniques have driven the evolution of time-domain OMA [1; 12]. For example, the random decrement technique estimates free vibration behavior from ambient or noisy measurements. Similarly, the natural excitation technique (NExT) isolates free vibration responses from forced responses under unknown excitations. Autoregressive models, such as autoregressive moving average (ARMA), predict output responses using past values to infer modal properties. Methods based on cross-power spectrum analysis identify modal parameters by examining frequency content and phase relationships between output signals. Moreover, the eigensystem realization algorithm (ERA) constructs state-space models and derives modal parameters from state-matrix eigenvalues. Last but not least, stochastic subspace identification (SSI) stands out for its ability to process large datasets and robustness against noise, eliminating the need for free-decay signals or cross-correlation functions. Among the time- and frequency-domain approaches available for OMA, SSI, in particular, has gained prominence due to its versatility in handling real-world structural monitoring challenges. Other advantages include the ability to process large datasets, applicability to linear systems, and inherent robustness against measurement noise and disturbances [13; 14]. Fundamental work on subspace-related methods was first carried out by [PERSON], a German mathematician, in 1890 [15]. Its solid mathematical basis was built on by a number of researchers--such as [PERSON] and [PERSON], [PERSON] and [PERSON], and so on--to exploit the Markov parameters of linear systems in the 1960s [15]. Then, some breakthroughs were made by [PERSON] and [PERSON], who systematically formulated the state-space-based method, discreetly developed theoretical frameworks to eliminate reliance on input measurements, and thoughtfully established implementation guidelines for the identification process [16; 17; 18].