  Structural Health Monitoring (SHM) provides an economic approach which aims
to enhance understanding the behavior of structures by continuously collects
data through multiple networked sensors attached to the structure. This data is
then utilized to gain insight into the health of a structure and make timely
and economic decisions about its maintenance. The generated SHM sensing data is
non-stationary and exists in a correlated multi-way form which makes the
batch/off-line learning and standard two-way matrix analysis unable to capture
all of these correlations and relationships. In this sense, the online tensor
data analysis has become an essential tool for capturing underlying structures
in higher-order datasets stored in a tensor $\mathcal{X} \in \mathbb{R} ^{I_1
\times \dots \times I_N} $. The CANDECOMP/PARAFAC (CP) decomposition has been
extensively studied and applied to approximate X by N loading matrices A(1), .
. . ,A(N) where N represents the order of the tensor. We propose a novel
algorithm, FP-CPD, to parallelize the CANDECOMP/PARAFAC (CP) decomposition of a
tensor $\mathcal{X} \in \mathbb{R} ^{I_1 \times \dots \times I_N} $. Our
approach is based on stochastic gradient descent (SGD) algorithm which allows
us to parallelize the learning process and it is very useful in online setting
since it updates $\mathcal{X}^{t+1}$ in one single step. Our SGD algorithm is
augmented with Nesterov's Accelerated Gradient (NAG) and perturbation methods
to accelerate and guarantee convergence. The experimental results using
laboratory-based and real-life structural datasets indicate fast convergence
and good scalability.
