Photodegradation modeling based on laboratory accelerated test data and predictions under outdoor weathering for polymeric materials

Photodegradation, driven primarily by ultraviolet (UV) radiation, is the primary cause of failure for organic paints and coatings, as well as many other products made from polymeric materials exposed to sunlight. Traditional methods of service life prediction involve the use of outdoor exposure in harsh UV environments (e.g., Florida and Arizona). Such tests, however, require too much time (generally many years) to do an evaluation. To overcome the shortcomings of traditional methods, scientists at the U.S. National Institute of Standards and Technology (NIST) conducted a multiyear research program to collect necessary data via scientifically-based laboratory accelerated tests. This paper presents the statistical modeling and analysis of the photodegradation data collected at NIST, and predictions of degradation for outdoor specimens that are subjected to weathering. The analysis involves identifying a physics/chemistry-motivated model that will adequately describe photodegradation paths. The model incorporates the effects of explanatory variables which are UV spectrum, UV intensity, temperature, and relative humidity. We use a nonlinear mixed-effects model to describe the sample paths. We extend the model to allow for dynamic covariates and compare predictions with specimens that were exposed in an outdoor environment where the explanatory variables are uncontrolled but recorded. We also discuss the findings from the analysis of the NIST data and some areas for future research

Distribution on Warp Maps for Alignment of Open and Closed Curves

Alignment of curve data is an integral part of their statistical analysis, and can be achieved using model- or optimization-based approaches. The parameter space is usually the set of monotone, continuous warp maps of a domain. Infinite-dimensional nature of the parameter space encourages sampling based approaches, which require a distribution on the set of warp maps. Moreover, the distribution should also enable sampling in the presence of important landmark information on the curves which constrain the warp maps. For alignment of closed and open curves in $\mathbb{R}^d, d=1,2,3$, possibly with landmark information, we provide a constructive, point-process based definition of a distribution on the set of warp maps of $[0,1]$ and the unit circle $\mathbb{S}^1$ that is (1) simple to sample from, and (2) possesses the desiderata for decomposition of the alignment problem with landmark constraints into multiple unconstrained ones. For warp maps on $[0,1]$, the distribution is related to the Dirichlet process. We demonstrate its utility by using it as a prior distribution on warp maps in a Bayesian model for alignment of two univariate curves, and as a proposal distribution in a stochastic algorithm that optimizes a suitable alignment functional for higher-dimensional curves. Several examples from simulated and real datasets are provided

Markov Chain Monte Carlo Based Analysis of Bearing Vibrations

The aim of the work in this thesis is to use bearing vibration data to infer the condition of bearings, in particular to detect the presence or absence of damage, and identify the location and cause of damage to parts of the bearing structure. Traditional methods of vibration analysis are evaluated and compared with Markov chain Monte Carlo (MCMC) methods. The vibration datasets come from a selection of bearings that have been run from new. After running-in bearings, some are allowed to continue running for several hours. Others have seeded defects applied to balls or bearing races, and are then run for a short time. These data are used to evaluate the effectiveness of time-domain, frequency-domain and MCMC methods in the field of bearing vibration analysis. Time-domain measures can detect the presence or absence of damage in most cases. Different defect types affect vibrations differently, and this can be seen in plots of vibration data. The conventional time-domain methods investigated take a discrete measure or measures over each data. They are simple to implement, but do not have the ability to detect these differences in vibrations, and therefore cannot detect the nature of damage. Analysis in the frequency-domain is based on the fast Fourier transform (FFT) and filtering. It is successful in detecting the nature of some defects. Bearings with some defect types, or with low levels of damage, are difficult to distinguish from undamaged bearings, and each defect type is better detected using different filtering. These differences suggest that prominent vibrations occur at modes of flexural vibration of the outer race, and that the inner race can be approximated as a rigid body. A classification scheme is implemented using a mixture of time-domain and frequency-domain measures. This scheme can correctly classify data from many - but not all - bearings, but it gives no information on the certainty of classifications. The findings from the time-domain and frequency-domain analysis have been well explored previously. In this thesis they are combined with Bayesian inference, using a correlation based measure of likelihood to infer bearing condition. MCMC methods are implemented using an adaptive Metropolis (AM) algorithm, existing models of bearing behaviour, and vibration data in the time-domain. MCMC outputs give estimations of the empirical marginal distribution of parameters, so that not only can parameter values - and therefore the underlying physical mechanism - be estimated, but uncertainties on these estimates can also be quantified. An aims of this thesis is to see whether MCMC methods can be used to infer properties of bearing condition. This thesis shows this is possible, but there are difficulties to overcome. In particular, the use of the correlation based measure of likelihood results in the chain failing to converge in some cases. These states are identifiable, as the likelihood is lower than when convergence occurs. Possible solutions to this problem are discussed. Analysis of MCMC outputs leads to model refinements to better measure bearing properties. Marginal distributions relating to vibration frequency have properties that allow the physical cause of vibration sources to be inferred. Using data in the time-domain has some advantages when separating the individual sources of these periodic vibrations. In the frequency domain some of these sources have harmonics or sidebands that coincide with predicted frequencies of other sources. In addition, some of these frequencies are not at their predicted values. This is not unexpected, as slippage and the effect of loads are known to alter these frequencies. The analysis of MCMC outputs allows the physical cause of discrepancies to be investigated. Vibrations during the normal operation of undamaged bearings have certain properties that differ from vibrations caused by bearing defects, and relevant parameters show these differences. Distributions of parameters relating to the amplitude and duration of vibrations caused by defects are shown to have a relationship to defect dimensions. Further development is required before defect dimensions can be directly inferred. This thesis shows that traditional methods of vibration analysis can distinguish between damaged and undamaged bearings in most cases, and detect the nature of damage in some cases. MCMC methods have potential in the field of bearing vibration analysis, and can provide meaningful inference of the physical properties of bearings