KEYWORDS: Filtering (signal processing), Interference (communication), Data fusion, Principal component analysis, Error analysis, Signal processing, Global Positioning System, Sensors, Time metrology, Data analysis
The Kalman filter is commonly employed to fuse the measured information from displacement and acceleration
responses. This fusion technique can mitigate the noise effect and produce more accurate response estimates. The fusion
performance however significantly depends on the accuracy of noise estimation. The noise variances are generally
estimated empirically a priori and assumed to be fixed throughout the calculation. Hence some estimation error might
occur when the noise characteristics are time-varying. In this study, an adaptive subspace-based technique is developed
to identify the noise variances. The approach is based on the principal component analysis which decomposes noisecontaminated
signals into the signal subspace and the noise subspace. The variances of the noise and signals can then be
estimated independently. To track the time variations of the noise and signal variances in an on-line fashion, a projection
approximation subspace tracking technique is employed. The proposed technique can be incorporated into an adaptive
Kalman filter and provide a more accurate estimation for data fusion.
KEYWORDS: Stochastic processes, Signal processing, Data processing, System identification, Detection and tracking algorithms, Filtering (signal processing), Digital filtering, Structural health monitoring, Performance modeling, Modal analysis
Identification of structural parameters under ambient condition is an important research topic for structural health
monitoring and damage identification. This problem is especially challenging in practice as these structural parameters
could vary with time under severe excitation. Among the techniques developed for this problem, the stochastic subspace
identification (SSI) is a popular time-domain method. The SSI can perform parametric identification for systems with
multiple outputs which cannot be easily done using other time-domain methods. The SSI uses the orthogonal-triangular
decomposition (RQ) and the singular value decomposition (SVD) to process measured data, which makes the algorithm
efficient and reliable. The SSI however processes data in one batch hence cannot be used in an on-line fashion. In this paper,
a recursive SSI method is proposed for on-line tracking of time-varying modal parameters for a structure under ambient
excitation. The Givens rotation technique, which can annihilate the designated matrix elements, is used to update the RQ
decomposition. Instead of updating the SVD, the projection approximation subspace tracking technique which uses an
unconstrained optimization technique to track the signal subspace is employed. The proposed technique is demonstrated on
the Phase I ASCE benchmark structure. Results show that the technique can identify and track the time-varying modal
properties of the building under ambient condition.
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