In this paper, we discuss the design considerations and challenges of using applied machine learning in complex systems, a necessity of operationalizing machine learning techniques. Although many applications of machine learning intend to discern key information insights from large collections of data, in realizable systems the quantity of insights may be so numerous that the insights remain as data and encumber a system and its users. New system design principles are emerging as a result of the dynamism of the machine learning community.
For classical simulation, the quantum Fourier transform (QFT) requires very large matrix operations. Previous
work has shown that the semi-classical quantum Fourier transform (SCQFT) can use these individual coefficients
to perform the QFT using only single-quantum bit (qubit) unitary gates and measurement operators. However,
the SCQFT requires these individual decomposed qubits of the quantum system as input to the algorithm. We
devise two methods to find separable approximations of quantum systems to serve as inputs to the SCQFT. We
introduce an application of the approach on classical radio frequency signals represented through a quantum
model. The resulting decomposition and QFT are computed on several simulated results, and an example is
given using an experimental signal.
Several data-driven features have recently proven to be successful at detecting damage in structures. Some of these
features, developed within the context of their state space attractors, highlight dynamics-specific changes without relying
on model-specific forms or assumptions such as linearity. Features such as generalized interdependence and state space
prediction error can also be formulated such that they provide information about generalized correlations between time
series. Therefore, in addition to damage indications, these features can also provide details about the location of damage
in a structure by comparing dynamical differences between measurements. This work proposes a framework for
establishing such an analysis procedure that can detect presence, extent, location, and/or type of damage in a structure
from a single feature. This approach is validated on a multi-degree of freedom oscillator.
Recently, damage sensitive features extracted from the phase space reconstruction of a structural response have
proven to be successful for use in the field of structural health monitoring. One such feature utilizes the evolutions of
randomly selected points on a baseline attractor to predict evolutions of corresponding points on an attractor in some
unknown state of health. The error based on this prediction can be used to determine the presence and/or extent of
damage. One drawback of this approach is that some regions of the attractor geometry may be more or less sensitive to
damage-induced changes in the dynamics. Thus, prediction error could incur large variances in its distribution, and
results could change significantly depending on the size and location of the randomly selected subset of points used for
prediction. This paper examines the effect of spatial location on prediction error in an effort to better utilize the geometry
of phase space. Investigations will involve a chaos-driven oscillator subject to parametric changes simulating damage.
Structural system identification, historically, has largely consisted of seeking linear relationships among vibration time series data, e.g., auto/cross-correlations, modal analysis, ARMA models, etc. This work considers how dynamical relationships may be viewed in terms of 'information flow' between different points on a structure. Information or interdependence metrics (e.g., time-delayed mutual information) are able to capture both linear and nonlinear aspects of the dynamics, including higher-order correlations. This work computes information-based metrics on a frame experiment where nonlinearity is introduced by the loosening of a bolt. Both linear and nonlinear measures of dynamical interdependence are then used to assess the degree of degradation to the joint. Results indicate clear differences in the way linear and nonlinear measures quantify the bolt loosening.
One paradigm within the structural health monitoring field involves analyzing the vibration response of structures as a method of detecting damage. Recent work has focused on extracting damage-sensitive features from the state-space representation of the structural response. Some of these features involve constructing a baseline attractor and an attractor at some later time and using the baseline to predict the evolution of the future attractor. An inability to accurately predict said evolution can be construed as possible damage to the structure. Such attractor-based methods are sensitive to a number of parameters related to reconstruction of the attractor, prediction techniques, and statistical accuracy. This work couples various input excitations with experimental data in an attempt to optimize these parameters for maximum sensitivity to damage.
Detection of the change in the vibration response of a structure as a means of damage detection has long been explored in the structural health monitoring field. Recently, damage detection metrics based on state-space attractor comparisons have been presented in the literature. This work compares various state-space attractor methods within an experimental context in an effort to determine the sensitivity of the methods to induced damage. The various methods are judged according to damage discrimination capability and computational effort.