Kernel methods for detecting coherent structures in dynamical data

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes (VAMP) score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition (DMD) called coherent mode decomposition (CMD). Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods

Learning Dynamic Systems for Intention Recognition in Human-Robot-Cooperation

This thesis is concerned with intention recognition for a humanoid robot and investigates how the challenges of uncertain and incomplete observations, a high degree of detail of the used models, and real-time inference may be addressed by modeling the human rationale as hybrid, dynamic Bayesian networks and performing inference with these models. The key focus lies on the automatic identification of the employed nonlinear stochastic dependencies and the situation-specific inference

Machine learning methods for uncertainty quantification in subsurface reservoirs

We investigate current challenges in the reservoir engineering pipeline that can be addressed using recent machine learning techniques. Our emphasis is on improving the performance of uncertainty quantification tasks which are ubiquitous in subsurface reservoir simulations. In one work, we accelerate multiscale methods by embedding a neural network surrogate for the fast computation of the custom basis functions, replacing the need to solve the local elliptic problems normally required to obtain them. In a different work, we address current challenges in obtaining geological parametrizations that can capture complex geological structures. We adopt a neural network parametrization using a recent unsupervised learning technique, obtaining an effective parametrization that can reproduce high-order statistics of flow responses. In a follow-up work, we introduce a method for post-hoc conditioning of the neural network parametrization to generate conditional realizations by training a second neural network to sample from a Bayesian posterior and coupling it with the original network. In our final work, we introduce a framework for exemplar-based parametric synthesis of geological images based on a recent kernel method, obtaining a neural network parametrization of the geology using a single exemplar image

Novel deep cross-domain framework for fault diagnosis or rotary machinery in prognostics and health management

Improving the reliability of engineered systems is a crucial problem in many applications in various engineering fields, such as aerospace, nuclear energy, and water declination industries. This requires efficient and effective system health monitoring methods, including processing and analyzing massive machinery data to detect anomalies and performing diagnosis and prognosis. In recent years, deep learning has been a fast-growing field and has shown promising results for Prognostics and Health Management (PHM) in interpreting condition monitoring signals such as vibration, acoustic emission, and pressure due to its capacity to mine complex representations from raw data. This doctoral research provides a systematic review of state-of-the-art deep learning-based PHM frameworks, an empirical analysis on bearing fault diagnosis benchmarks, and a novel multi-source domain adaptation framework. It emphasizes the most recent trends within the field and presents the benefits and potentials of state-of-the-art deep neural networks for system health management. Besides, the limitations and challenges of the existing technologies are discussed, which leads to opportunities for future research. The empirical study of the benchmarks highlights the evaluation results of the existing models on bearing fault diagnosis benchmark datasets in terms of various performance metrics such as accuracy and training time. The result of the study is very important for comparing or testing new models. A novel multi-source domain adaptation framework for fault diagnosis of rotary machinery is also proposed, which aligns the domains in both feature-level and task-level. The proposed framework transfers the knowledge from multiple labeled source domains into a single unlabeled target domain by reducing the feature distribution discrepancy between the target domain and each source domain. Besides, the model can be easily reduced to a single-source domain adaptation problem. Also, the model can be readily updated to unsupervised domain adaptation problems in other fields such as image classification and image segmentation. Further, the proposed model is modified with a novel conditional weighting mechanism that aligns the class-conditional probability of the domains and reduces the effect of irrelevant source domain which is a critical issue in multi-source domain adaptation algorithms. The experimental verification results show the superiority of the proposed framework over state-of-the-art multi-source domain-adaptation models

Information Theory and Its Application in Machine Condition Monitoring

Condition monitoring of machinery is one of the most important aspects of many modern industries. With the rapid advancement of science and technology, machines are becoming increasingly complex. Moreover, an exponential increase of demand is leading an increasing requirement of machine output. As a result, in most modern industries, machines have to work for 24 hours a day. All these factors are leading to the deterioration of machine health in a higher rate than before. Breakdown of the key components of a machine such as bearing, gearbox or rollers can cause a catastrophic effect both in terms of financial and human costs. In this perspective, it is important not only to detect the fault at its earliest point of inception but necessary to design the overall monitoring process, such as fault classification, fault severity assessment and remaining useful life (RUL) prediction for better planning of the maintenance schedule. Information theory is one of the pioneer contributions of modern science that has evolved into various forms and algorithms over time. Due to its ability to address the non-linearity and non-stationarity of machine health deterioration, it has become a popular choice among researchers. Information theory is an effective technique for extracting features of machines under different health conditions. In this context, this book discusses the potential applications, research results and latest developments of information theory-based condition monitoring of machineries

Machine Learning

Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience

Multilevel Delayed Acceptance MCMC with Applications to Hydrogeological Inverse Problems

Quantifying the uncertainty of model predictions is a critical task for engineering decision support systems. This is a particularly challenging effort in the context of statistical inverse problems, where the model parameters are unknown or poorly constrained, and where the data is often scarce. Many such problems emerge in the fields of hydrology and hydro--environmental engineering in general, and in hydrogeology in particular. While methods for rigorously quantifying the uncertainty of such problems exist, they are often prohibitively computationally expensive, particularly when the forward model is high--dimensional and expensive to evaluate. In this thesis, I present a Metropolis--Hastings algorithm, namely the Multilevel Delayed Acceptance (MLDA) algorithm, which exploits a hierarchy of forward models of increasing computational cost to significantly reduce the total cost of quantifying the uncertainty of high--dimensional, expensive forward models. The algorithm is shown to be in detailed balance with the posterior distribution of parameters, and the computational gains of the algorithm is demonstrated on multiple examples. Additionally, I present an approach for exploiting a deep neural network as an ultra--fast model approximation in an MLDA model hierarchy. This method is demonstrated in the context of both 2D and 3D groundwater flow modelling. Finally, I present a novel approach to adaptive optimal design of groundwater surveying, in which MLDA is employed to construct the posterior Monte Carlo estimates. This method utilises the posterior uncertainty of the primary problem in conjunction with the expected solution to an adjoint problem to sequentially determine the optimal location of the next datapoint.Engineering and Physical Sciences Research Council (EPSRC)Alan Turing InstituteEngineering and Physical Sciences Research Council (EPSRC