Herein, we propose a method based on the existing second-order blind identification of underdetermined mixtures technique for identifying the modal characteristics-namely, natural frequencies, damping ratio, and real-valued partial mode shapes of all contributing modes-of structures with a limited number of sensors from recorded free/ ambient vibration data. In the second-order blind identification approach, second-order statistics of recorded signals are used to recover modal coordinates and mode shapes. Conventional versions of this approach require the number of sensors to be equal to or greater than the number of active modes. In the present study, we first employ a parallel factor technique to decompose the covariance tensor into rank-one tensors so that the partial mode shapes at the recording locations (sensors) can be estimated. The mode shape matrix identified in this manner is not square, which precludes the use of a simple inversion to extract the modal coordinates. As such, the natural frequencies are identified from the recovered modal coordinates' Autocovariances. The damping ratios are extracted using a least-squares technique from modal free vibrations, as they are not directly recoverable because of the inherent smearing produced by windowing processes. Finally, a Bayesian model updating approach is employed to complete the partial mode shapes-that is, to extract the mode shapes at the DOFs without sensors. We use simulated and physical data for verifying and validating this new identification method, and explore optimal sensor distribution in multistory structures for a given (limited) number of sensors. particular extraction method works without having the sources or the mixing processes-hence, the term blind-and employs second-order statistics of recorded response signals to recover the modal coordinate signals and the mode shape matrix. However, SOBI method does not work well in the presence of highly damped, low-energy or closely spaced modes, severe nonstationary excitations, and relatively large measurement noise. The issues of weakly nonstationary signals and noisy measurement were addressed in [20], whereas separability of low-energy modes was improved by employing stationary wavelet transform in [21]. Nevertheless, conventional versions of SOBI methods are limited to determined or overdetermined problems, in which the number of active modes is equal to or less than the number of recorded signals. For civil structures (e.g., tall buildings, long-span bridges, etc.), this constraint is often prohibitive.Various algorithms are presented in the signal processing literature for underdetermined problems, and in most such studies, the source signals (here, the modal coordinates) are assumed to be sparse [22,23]. Given this condition, time-frequency representations along with clustering techniques [24,25] or modal decompositions [26] are used to identify the source signals. Nevertheless, aforementioned methods are not suitable for modal identification of civil structures because their free or a...
SUMMARY Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.
SUMMARY Response‐only identification of civil structures has attracted much attention during recent years, as input excitations are rarely measurable for ambient vibrations. Although various techniques have been developed by which identification can be carried out using ambient responses, these techniques are generally not applicable to non‐stationary excitations that structures experience during moderate‐to‐severe earthquakes. Recently, the authors proposed a new response‐only modal identification method that is applicable to strong shaking data. This new method is highly attractive for cases in which the true input motions are unavailable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded foundation responses may be assumed as input. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with low signal‐to‐noise ratios). Thus far, the said method has been only applicable to fully instrumented systems wherein the number of sensors is equal to or greater than the number of active modes. In this study, we offer various improvements, including an extension that enables the treatment of sparsely instrumented systems. Specifically, a cluster‐based underdetermined time–frequency method is employed at judiciously selected auto‐source points to determine the mode shapes. The mode shape matrix identified in this manner is not square, which precludes the use of simple matrix inversion to extract the modal coordinates. As such, natural frequencies and damping ratios are identified from the recovered modal coordinates' time–frequency distributions using a subspace method. Simulated data are used for verifying the proposed identification method. Copyright © 2013 John Wiley & Sons, Ltd.
SUMMARYThe Robert A. Millikan Library is a reinforced concrete building with a basement level and nine stories above the ground. Located on the campus of California Institute of Technology (Caltech) in Pasadena California, it is among the most densely instrumented buildings in the U.S. From the early dates of its construction, it has been the subject of many investigations, especially regarding soil-structure interaction effects. It is well accepted that the structure is significantly interacting with the surrounding soil, which implies that the true foundation input motions cannot be directly recorded during earthquakes because of inertial effects. Based on this limitation, input-output modal identification methods are not applicable to this soil-structure system. On the other hand, conventional outputonly methods are typically based on the unknown input signals to be stationary whitenoise, which is not the case for earthquake excitations. Through the use of recently developed blind identification (i.e. output-only) methods, it has become possible to extract such information from only the response signals because of earthquake excitations. In the present study, we employ such a blind identification method to extract the modal properties of the Millikan Library. We present some modes that have not been identified from force vibration tests in several studies to date. Then, to quantify the contribution of soil-structure interaction effects, we first create a detailed Finite Element (FE) model using available information about the superstructure; and subsequently update the soil-foundation system's dynamic stiffnesses at each mode such that the modal properties of the entire soil-structure system agree well with those obtained via output-only modal identification.
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