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- Creators: Brake, Matt
Description
The present investigation is part of a long-term effort focused on the development of a methodology for the computationally efficient prediction of the dynamic response of structures with multiple joints. The first part of this thesis reports on the dynamic response of nominally identical beams with a single lap joint (“Brake-Reuss” beam). The observed impact responses at different levels clearly demonstrate the occurrence of both micro- and macro-slip, which are reflected by increased damping and a lowering of natural frequencies. Significant beam-to-beam variability of impact responses is also observed.
Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.
The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.
The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.
Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.
The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.
The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.
ContributorsRobertson, Brett Anthony (Author) / Mignolet, Marc P (Thesis advisor) / Brake, Matt (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016
Description
Feature learning and the discovery of nonlinear variation patterns in high-dimensional data is an important task in many problem domains, such as imaging, streaming data from sensors, and manufacturing. This dissertation presents several methods for learning and visualizing nonlinear variation in high-dimensional data. First, an automated method for discovering nonlinear variation patterns using deep learning autoencoders is proposed. The approach provides a functional mapping from a low-dimensional representation to the original spatially-dense data that is both interpretable and efficient with respect to preserving information. Experimental results indicate that deep learning autoencoders outperform manifold learning and principal component analysis in reproducing the original data from the learned variation sources.
A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem.
An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns.
Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets.
A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem.
An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns.
Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets.
ContributorsHoward, Phillip (Author) / Runger, George C. (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Mirchandani, Pitu (Committee member) / Apley, Daniel (Committee member) / Arizona State University (Publisher)
Created2016