Robust fault detection based on adaptive threshold generation using interval LPV observers

In this paper, robust fault detection based on adaptive threshold generation of a non-linear system described by means of a linear parameter-varying (LPV) model is addressed. Adaptive threshold is generated using an interval LPV observer that generates a band of predicted outputs taking into account the parameter uncertainties bounded using intervals. An algorithm that propagates the uncertainty based on zonotopes is proposed. The design procedure of this interval LPV observer is implemented via pole placement using linear matrix inequalities. Finally, the minimum detectable fault is characterized using fault sensitivity analysis and residual uncertainty bounds. Two examples, one based on a quadruple-tank system and another based on a two-degree of freedom helicopter, are used to assess the validity of the proposed fault detection approach.Postprint (published version

Robust and Optimal Methods for Geometric Sensor Data Alignment

Geometric sensor data alignment - the problem of finding the rigid transformation that correctly aligns two sets of sensor data without prior knowledge of how the data correspond - is a fundamental task in computer vision and robotics. It is inconvenient then that outliers and non-convexity are inherent to the problem and present significant challenges for alignment algorithms. Outliers are highly prevalent in sets of sensor data, particularly when the sets overlap incompletely. Despite this, many alignment objective functions are not robust to outliers, leading to erroneous alignments. In addition, alignment problems are highly non-convex, a property arising from the objective function and the transformation. While finding a local optimum may not be difficult, finding the global optimum is a hard optimisation problem. These key challenges have not been fully and jointly resolved in the existing literature, and so there is a need for robust and optimal solutions to alignment problems. Hence the objective of this thesis is to develop tractable algorithms for geometric sensor data alignment that are robust to outliers and not susceptible to spurious local optima. This thesis makes several significant contributions to the geometric alignment literature, founded on new insights into robust alignment and the geometry of transformations. Firstly, a novel discriminative sensor data representation is proposed that has better viewpoint invariance than generative models and is time and memory efficient without sacrificing model fidelity. Secondly, a novel local optimisation algorithm is developed for nD-nD geometric alignment under a robust distance measure. It manifests a wider region of convergence and a greater robustness to outliers and sampling artefacts than other local optimisation algorithms. Thirdly, the first optimal solution for 3D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms other geometric alignment algorithms on challenging datasets due to its guaranteed optimality and outlier robustness, and has an efficient parallel implementation. Fourthly, the first optimal solution for 2D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms existing approaches on challenging datasets, reliably finding the global optimum, and has an efficient parallel implementation. Finally, another optimal solution is developed for 2D-3D geometric alignment, using a robust surface alignment measure. Ultimately, robust and optimal methods, such as those in this thesis, are necessary to reliably find accurate solutions to geometric sensor data alignment problems

Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method

We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to $\mathbb{R}^3$ of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI: 10.1016/j.jcp.2022.111291][2]. However, in contrast to [1,2], which built resolution-dependent neural-network dictionaries, here we develop a pair of models in $\mathbb{R}^3$, regardless of the mesh size. Our feedforward networks ingest transformed level-set, gradient, and curvature data to fix numerical mean-curvature approximations selectively for interface nodes. To reduce the problem's complexity, we have used the Gaussian curvature to classify stencils and fit our models separately to non-saddle and saddle patterns. Non-saddle stencils are easier to handle because they exhibit a curvature error distribution characterized by monotonicity and symmetry. While the latter has allowed us to train only on half the mean-curvature spectrum, the former has helped us blend the data-driven and the baseline estimations seamlessly near flat regions. On the other hand, the saddle-pattern error structure is less clear; thus, we have exploited no latent information beyond what is known. In this regard, we have trained our models on not only spherical but also sinusoidal and hyperbolic paraboloidal patches. Our approach to building their data sets is systematic but gleans samples randomly while ensuring well-balancedness. We have also resorted to standardization and dimensionality reduction and integrated regularization to minimize outliers. In addition, we leverage curvature rotation/reflection invariance to improve precision at inference time. Several experiments confirm that our proposed system can yield more accurate mean-curvature estimations than modern particle-based interface reconstruction and level-set schemes around under-resolved regions

Advanced similarity queries and their application in data mining

Ph.DDOCTOR OF PHILOSOPH

Paraglide: Interactive Parameter Space Partitioning for Computer Simulations

In this paper we introduce paraglide, a visualization system designed for interactive exploration of parameter spaces of multi-variate simulation models. To get the right parameter configuration, model developers frequently have to go back and forth between setting parameters and qualitatively judging the outcomes of their model. During this process, they build up a grounded understanding of the parameter effects in order to pick the right setting. Current state-of-the-art tools and practices, however, fail to provide a systematic way of exploring these parameter spaces, making informed decisions about parameter settings a tedious and workload-intensive task. Paraglide endeavors to overcome this shortcoming by assisting the sampling of the parameter space and the discovery of qualitatively different model outcomes. This results in a decomposition of the model parameter space into regions of distinct behaviour. We developed paraglide in close collaboration with experts from three different domains, who all were involved in developing new models for their domain. We first analyzed current practices of six domain experts and derived a set of design requirements, then engaged in a longitudinal user-centered design process, and finally conducted three in-depth case studies underlining the usefulness of our approach

IMAGE ANALYSIS FOR SPINE SURGERY: DATA-DRIVEN DETECTION OF SPINE INSTRUMENTATION & AUTOMATIC ANALYSIS OF GLOBAL SPINAL ALIGNMENT

Spine surgery is a therapeutic modality for treatment of spine disorders, including spinal deformity, degeneration, and trauma. Such procedures benefit from accurate localization of surgical targets, precise delivery of instrumentation, and reliable validation of surgical objectives – for example, confirming that the surgical implants are delivered as planned and desired changes to the global spinal alignment (GSA) are achieved. Recent advances in surgical navigation have helped to improve the accuracy and precision of spine surgery, including intraoperative imaging integrated with real-time tracking and surgical robotics. This thesis aims to develop two methods for improved image-guided surgery using image analytic techniques. The first provides a means for automatic detection of pedicle screws in intraoperative radiographs – for example, to streamline intraoperative assessment of implant placement. The algorithm achieves a precision and recall of 0.89 and 0.91, respectively, with localization accuracy within ~10 mm. The second develops two algorithms for automatic assessment of GSA in computed tomography (CT) or cone-beam CT (CBCT) images, providing a means to quantify changes in spinal curvature and reduce the variability in GSA measurement associated with manual methods. The algorithms demonstrate GSA estimates with 93.8% of measurements within a 95% confidence interval of manually defined truth. Such methods support the goals of safe, effective spine surgery and provide a means for more quantitative intraoperative quality assurance. In turn, the ability to quantitatively assess instrument placement and changes in GSA could represent important elements of retrospective analysis of large image datasets, improved clinical decision support, and improved patient outcomes