Vibration-based condition monitoring is a key and crucial element for asset longevity and to avoid unexpected financial compromise. Currently, data-driven methodologies often require significant investments into data acquisition and a large amount of operational data for both healthy and unhealthy cases. The acquisition of unhealthy fault data is often financially infeasible and the result is that most methods detailed in literature are not suitable for critical industrial applications. In this work, unsupervised latent variable models negate the requirement for asset fault data. These models operate by learning the representation of healthy data and utilise health indicators to track deviance from this representation. A variety of latent variable models are compared, namely: Principal Component Analysis, Variational Auto-Encoders and Generative Adversarial Network-based methods. This research investigated the relationship between time-series data and latent variable model design under the sensible notion of data interpretation, the influence of model complexity on result performance on different datasets and shows that the latent manifold, when untangled and traversed in a sensible manner, is indicative of damage. Three latent health indicators are proposed in this work and utilised in conjunction with a proposed temporal preservation approach. The performance is compared over the different models. It was found that these latent health indicators can augment standard health indicators and benefit model performance. This allows one to compare the performance of different latent variable models, an approach that has not been realised in previous work as the interpretation of the latent manifold and the manifold response to anomalous instances had not been explored. If all aspects of a latent variable model are systematically investigated and compared, different models can be analysed on a consistent platform. In the model analysis step, a latent variable model is used to evaluate the available data such that the health indicators used to infer the health state of an asset, are available for analysis and comparison. The datasets investigated in this work consist of stationary and time-varying operating conditions. The objective was to determine whether deep learning is comparable or on par with state-of-the-art signal processing techniques. The results showed that damage is detectable in both the input space and the latent space and can be trended to identify clear condition deviance points. This highlights that both spaces are indicative of damage when analysed in a sensible manner. A key take away from this work is that for data that contains impulsive components that manifest naturally and not due to the presence of a fault, the anomaly detection procedure may be limited by inherent assumptions made in model formulations concerning Gaussianity. This work illustrates how the latent manifold is useful for the detection of anomalous instances, how one must consider a variety of latent-variable model types and how subtle changes to data processing can benefit model performance analysis substantially. For vibration-based condition monitoring, latent variable models offer significant improvements in fault diagnostics and reduce the requirement for expert knowledge. This can ultimately improve asset longevity and the investment required from businesses in asset maintenance. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2020. / Eskom Power Plant Engineering Institute (EPPEI) / UP Postgraduate Bursary / Mechanical and Aeronautical Engineering / MEng (Mechanical Engineering) / Unrestricted

This thesis investigates the application of latent variable methods to three combustion processes. Multivariate analysis of flame images and process data is performed to predict important quality parameters and monitor flame stability. The motivation behind this work is to decrease operational costs and greenhouse gases in these energy intensive processes. The three combustion processes studied are a lime kiln, a basic oxygen furnace and a coal-fired boiler. In lime kiln operation, the main goal is to stabilize final product temperature in order to reduce fouling and energy costs. Due to long process dynamics, prediction of product temperature is required at least one hour in advance for potential use in a control scheme. Several methods for extracting features from flame images were investigated for the prediction of the temperature. The best method is then combined with process data in a PLS model that also incorporates dynamic information. The analysis revealed that prediction one hour into the future is successful using latent variable methods. In the basic oxygen furnace analysis, the main goal is to predict end-point carbon of the batch process. Termination of the batch as soon as the desired carbon is attained reduces oxygen consumption and thus operational cost. Traditional image analysis is used to identify a constant field of view in the flame images. Multivariate image feature extraction methods were then used in combination with process data to successfully predict the final carbon content of the heat. The coal-fired boiler analysis focuses on monitoring of flame stability at different production and air to fuel levels of the boiler. Prediction of energy efficiency and off-gas chemistry from flame images is also investigated. An unexpected result was the ability to use the installed cameras for localized fouling monitoring. This thesis showed that the use of multivariate analysis of flame images and process data in combustion process is very promising. / Thesis / Master of Applied Science (MASc)

<p>Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging. </p>

Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging.

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Two important components of a visual recognition system are representation and model. Both involves the selection and learning of the features that are indicative for recognition and discarding those features that are uninformative. This thesis, in its general form, proposes different techniques within the frameworks of two learning systems for representation and modeling. Namely, latent support vector machines (latent SVMs) and deep learning. First, we propose various approaches to group the positive samples into clusters of visually similar instances. Given a fixed representation, the sampled space of the positive distribution is usually structured. The proposed clustering techniques include a novel similarity measure based on exemplar learning, an approach for using additional annotation, and augmenting latent SVM to automatically find clusters whose members can be reliably distinguished from background class.  In another effort, a strongly supervised DPM is suggested to study how these models can benefit from privileged information. The extra information comes in the form of semantic parts annotation (i.e. their presence and location). And they are used to constrain DPMs latent variables during or prior to the optimization of the latent SVM. Its effectiveness is demonstrated on the task of animal detection. Finally, we generalize the formulation of discriminative latent variable models, including DPMs, to incorporate new set of latent variables representing the structure or properties of negative samples. Thus, we term them as negative latent variables. We show this generalization affects state-of-the-art techniques and helps the visual recognition by explicitly searching for counter evidences of an object presence. Following the resurgence of deep networks, in the last works of this thesis we have focused on deep learning in order to produce a generic representation for visual recognition. A Convolutional Network (ConvNet) is trained on a largely annotated image classification dataset called ImageNet with $\sim1.3$ million images. Then, the activations at each layer of the trained ConvNet can be treated as the representation of an input image. We show that such a representation is surprisingly effective for various recognition tasks, making it clearly superior to all the handcrafted features previously used in visual recognition (such as HOG in our first works on DPM). We further investigate the ways that one can improve this representation for a task in mind. We propose various factors involving before or after the training of the representation which can improve the efficacy of the ConvNet representation. These factors are analyzed on 16 datasets from various subfields of visual recognition. / <p>QC 20160908</p>

Neste trabalho apresentamos os mais importantes processos de estimação em algumas classes de modelos de resposta ao item (Dicotômicos e Policotômicos). Discutimos algumas propriedades desses métodos. Com o objetivo de comparar o desempenho dos métodos conduzimos simulações apropriadas. / In this work we show the most important estimation methods for some item response models (both dichotomous and polichotomous). We discuss some proprieties of these methods. To compare the characteristic of these methods we conducted appropriate simulations.

Neste trabalho apresentamos os mais importantes processos de estimação em algumas classes de modelos de resposta ao item (Dicotômicos e Policotômicos). Discutimos algumas propriedades desses métodos. Com o objetivo de comparar o desempenho dos métodos conduzimos simulações apropriadas. / In this work we show the most important estimation methods for some item response models (both dichotomous and polichotomous). We discuss some proprieties of these methods. To compare the characteristic of these methods we conducted appropriate simulations.

A Monte Carlo simulation study on class enumeration with latent class regression models. / Latent class regression (LCR) is a statistical method used to identify qualitatively different groups or latent classes within a heterogeneous population and commonly used in the behavioural, health, and social sciences. Despite the vast applications, an agreed fit index to correctly determine the number of latent classes is hotly debated. To add, there are also conflicting views on whether covariates should or should not be included into the class enumeration process. We conduct a simulation study to determine the impact of covariates on the class enumeration accuracy as well as study the performance of several commonly used fit indices under different population models and modelling conditions. Our results indicate that of the eight fit indices considered, the aBIC and BLRT proved to be the best performing fit indices for class enumeration. Furthermore, we found that covariates should not be included into the enumeration procedure. Our results illustrate that an unconditional LCA model can enumerate equivalently as well as a conditional LCA model with its true covariate specification. Even with the presence of large covariate effects in the population, the unconditional model is capable of enumerating with high accuracy. As noted by Nylund and Gibson (2016), a misspecified covariate specification can easily lead to an overestimation of latent classes. Therefore, we recommend to perform class enumeration without covariates and determine a set of candidate latent class models with the aBIC. Once that is determined, the BLRT can be utilized on the set of candidate models and confirm whether results obtained by the BLRT match the results of the aBIC. By separating the enumeration procedure of the BLRT, it still allows one to use the BLRT but reduce the heavy computational burden that is associated with this fit index. Subsequent analysis can then be pursued accordingly after the number of latent classes is determined. / Thesis / Master of Science (MSc)

Cette thèse a pour objectif d’incorporer des éléments de théories de psychologie et d’économie comportementale dans des modèles de choix discret afin d’améliorer la compréhension du choix modal réalisé à l’échelle régionale. Les estimations se basent sur une enquête de type choice experiment présentée en première partie. Une deuxième partie s’intéresse à l’incorporation de variables latentes pour expliquer le choix modal. Après une revue de littérature sur les modèles de choix hybrides, c’est-à-dire des modèles combinant modèle d’équations structurelles et modèle de choix discret, un tel modèle est estimé pour montrer comment l’hétérogénéité d’outputs économiques (ici, la valeur du temps) peut être expliquée à l’aide de variables latentes (ici, le confort perçu dans les transports en commun) et de variables observables (ici, la garantie d’une place assise). La simulation de scénarios montre cependant que le gain économique (diminution de la valeur du temps) est plus élevé lorsque les politiques agissent sur des dimensions palpables que sur des dimensions latentes. S’appuyant sur un modèle de médiation, l’estimation d’un modèle d’équations structurelles montre par ailleurs que l’effet de la conscience environnementale sur les habitudes de choix modal est partiellement médié par l’utilité indirecte retirée de l’usage des transports en commun. Une troisième partie s’intéresse à deux formalisations de l’utilité issues de l’économie comportementale : 1) l’utilité dépendante au rang en situation de risque et 2) l’utilité dépendante à la référence. Dans un premier temps, un modèle d’utilité dépendante au rang est inséré dans des modèles de choix discret et, en particulier, un modèle à classes latentes, afin d’analyser l’hétérogénéité intra- et inter-individuelle lorsque le temps de déplacement n’est pas fiable. La probabilité de survenue d’un retard est sur-évaluée pour les déplacements en train et sous-évaluée pour les déplacements en voiture, en particulier pour les automobilistes, les usagers du train prenant d’avantage en compte l’espérance du temps de déplacement. Dans les modèles prenant en compte l’aversion au risque, les fonctions d’utilité sont convexes, ce qui implique une décroissance,de la valeur du temps. Dans un deuxième temps, une nouvelle famille de modèles de choix discret généralisant le modèle logit multinomial, les modèles de référence, est estimée. Sur mes données, ces modèles permettent une meilleure sélection des variables explicatives que le logit multinomial et l’estimation d’outputs économiques plus robustes, notamment en cas de forte hétérogénéité inobservée. La traduction économique des modèles de référence montre que les meilleurs modèles empiriques sont également les plus compatibles avec le modèle de dépendance à la référence de Tversky et Kahneman. / The objective of this thesis is to incorporate aspects of psychology and behavioral economics theories in discrete choice models to promote a better understanding of mode choice at regional level. Part II examines the inclusion of latent variables to explain mode choice. A literature review of integrated choice and latent variable models – that is, models combining a structural equation model and a discrete choice model – is followed by the estimation of an integrated choice and latent variable model to show how the heterogeneity of economic outputs (here, value of time) can be explained with latent variables (here, perceived comfort in public transport) and observable variables (here, the guarantee of a seat). The simulation of scenarios shows, however, that the economic gain (decrease in value of time) is higher when policies address tangible factors than when they address latent factors. On the basis of a mediation model, the estimation of a structural equation model furthermore implies that the influence of environmental concern on mode choice habits is partially mediated by the indirect utility derived frompublic transport use. Part III examines two utility formulations taken from behavioral economics: 1) rankdependent utility to model risky choices, and 2) reference-dependent utility. Firstly, a rank-dependent utility model is included in discrete choice models and, in particular, a latent-class model, in order to analyze intra- and inter-individual heterogeneity when the travel time is subject to variability. The results show that the probability of a delay is over-estimated for train travel and under-estimated for car travel, especially for car users, as train users are more likely to take into account the expected travel time. In the models that account for risk aversion, the utility functions are convex, which implies a decrease in value of time. Secondly, a new family of discrete choice models generalizing the multinomial logit model, the reference models, is estimated. On my data, these models allow for a better selection of explanatory variables than the multinomial logit model and a more robust estimation of economic outputs, particularly in cases of high unobserved heterogeneity. The economic formulation of reference models shows thatthe best empirical models are also more compatible with Tversky et Kahneman’s reference-dependent model.