Asymptotic identification uncertainty of close modes in Bayesian operational modal analysis

This is the final version. Available on open access from Elsevier via the DOI in this recordClose modes are not typical subjects in operational modal analysis (OMA) but they do occur in structures with modes of similar dynamic properties such as tall buildings and towers. Compared to well-separated modes they are much more challenging to identify and results can have significantly higher uncertainty especially in the mode shapes. There are algorithms for identification (ID) and uncertainty calculation but the value itself does not offer any insight on ID uncertainty, which is necessary for its management in ambient test planning. Following a Bayesian approach, this work investigates analytically the ID uncertainty of close modes under asymptotic conditions of long data and high signal-to-noise ratio, which are nevertheless typical in applications. Asymptotic expressions for the Fisher Information Matrix (FIM), whose inverse gives the asymptotic ‘posterior’ (i.e., given data) covariance matrix of modal parameters, are derived explicitly in terms of governing dynamic properties. By investigating analytically the eigenvalue properties of FIM, we show that mode shape uncertainty occurs in two characteristic types of mutually uncorrelated principal directions, one perpendicular (Type 1) and one within the ‘mode shape subspace’ spanned by the mode shapes (Type 2). Uncertainty of Type 1 was found previously in well-separated modes. It is uncorrelated from other modal parameters (e.g., frequency and damping), diminishes with increased data quality and is negligible in applications. Uncertainty of Type 2 is a new discovery unique to close modes. It is potentially correlated with all modal parameters and does not vanish even for noiseless data. It reveals the intrinsic complexity and governs the achievable precision limit of OMA with close modes. Theoretical findings are verified numerically and applied with field data. This work has not reached the ultimate goal of ‘uncertainty law’, i.e., explicitly relating ID uncertainty to test configuration for understanding and test planning, but the analytical expressions of FIM and understanding about its eigenvalue properties shed light on possibility and provide the pathway to it.Engineering and Physical Sciences Research Council (EPSRC

DELO: Deep Evidential LiDAR Odometry using Partial Optimal Transport

Accurate, robust, and real-time LiDAR-based odometry (LO) is imperative for many applications like robot navigation, globally consistent 3D scene map reconstruction, or safe motion-planning. Though LiDAR sensor is known for its precise range measurement, the non-uniform and uncertain point sampling density induce structural inconsistencies. Hence, existing supervised and unsupervised point set registration methods fail to establish one-to-one matching correspondences between LiDAR frames. We introduce a novel deep learning-based real-time (approx. 35-40ms per frame) LO method that jointly learns accurate frame-to-frame correspondences and model's predictive uncertainty (PU) as evidence to safe-guard LO predictions. In this work, we propose (i) partial optimal transportation of LiDAR feature descriptor for robust LO estimation, (ii) joint learning of predictive uncertainty while learning odometry over driving sequences, and (iii) demonstrate how PU can serve as evidence for necessary pose-graph optimization when LO network is either under or over confident. We evaluate our method on KITTI dataset and show competitive performance, even superior generalization ability over recent state-of-the-art approaches. Source codes are available.Comment: Accepted in ICCV 2023 Worksho

Reasoning with Uncertainty in Deep Learning for Safer Medical Image Computing

Deep learning is now ubiquitous in the research field of medical image computing. As such technologies progress towards clinical translation, the question of safety becomes critical. Once deployed, machine learning systems unavoidably face situations where the correct decision or prediction is ambiguous. However, the current methods disproportionately rely on deterministic algorithms, lacking a mechanism to represent and manipulate uncertainty. In safety-critical applications such as medical imaging, reasoning under uncertainty is crucial for developing a reliable decision making system. Probabilistic machine learning provides a natural framework to quantify the degree of uncertainty over different variables of interest, be it the prediction, the model parameters and structures, or the underlying data (images and labels). Probability distributions are used to represent all the uncertain unobserved quantities in a model and how they relate to the data, and probability theory is used as a language to compute and manipulate these distributions. In this thesis, we explore probabilistic modelling as a framework to integrate uncertainty information into deep learning models, and demonstrate its utility in various high-dimensional medical imaging applications. In the process, we make several fundamental enhancements to current methods. We categorise our contributions into three groups according to the types of uncertainties being modelled: (i) predictive; (ii) structural and (iii) human uncertainty. Firstly, we discuss the importance of quantifying predictive uncertainty and understanding its sources for developing a risk-averse and transparent medical image enhancement application. We demonstrate how a measure of predictive uncertainty can be used as a proxy for the predictive accuracy in the absence of ground-truths. Furthermore, assuming the structure of the model is flexible enough for the task, we introduce a way to decompose the predictive uncertainty into its orthogonal sources i.e. aleatoric and parameter uncertainty. We show the potential utility of such decoupling in providing a quantitative “explanations” into the model performance. Secondly, we introduce our recent attempts at learning model structures directly from data. One work proposes a method based on variational inference to learn a posterior distribution over connectivity structures within a neural network architecture for multi-task learning, and share some preliminary results in the MR-only radiotherapy planning application. Another work explores how the training algorithm of decision trees could be extended to grow the architecture of a neural network to adapt to the given availability of data and the complexity of the task. Lastly, we develop methods to model the “measurement noise” (e.g., biases and skill levels) of human annotators, and integrate this information into the learning process of the neural network classifier. In particular, we show that explicitly modelling the uncertainty involved in the annotation process not only leads to an improvement in robustness to label noise, but also yields useful insights into the patterns of errors that characterise individual experts

Perceptual Factors for Environmental Modeling in Robotic Active Perception

Accurately assessing the potential value of new sensor observations is a critical aspect of planning for active perception. This task is particularly challenging when reasoning about high-level scene understanding using measurements from vision-based neural networks. Due to appearance-based reasoning, the measurements are susceptible to several environmental effects such as the presence of occluders, variations in lighting conditions, and redundancy of information due to similarity in appearance between nearby viewpoints. To address this, we propose a new active perception framework incorporating an arbitrary number of perceptual effects in planning and fusion. Our method models the correlation with the environment by a set of general functions termed perceptual factors to construct a perceptual map, which quantifies the aggregated influence of the environment on candidate viewpoints. This information is seamlessly incorporated into the planning and fusion processes by adjusting the uncertainty associated with measurements to weigh their contributions. We evaluate our perceptual maps in a simulated environment that reproduces environmental conditions common in robotics applications. Our results show that, by accounting for environmental effects within our perceptual maps, we improve in the state estimation by correctly selecting the viewpoints and considering the measurement noise correctly when affected by environmental factors. We furthermore deploy our approach on a ground robot to showcase its applicability for real-world active perception missions.Comment: 7 pages, 9 figures, under review for IEEE ICRA 202

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Autonomous Recharging and Flight Mission Planning for Battery-operated Autonomous Drones

Autonomous drones (also known as unmanned aerial vehicles) are increasingly popular for diverse applications of light-weight delivery and as substitutions of manned operations in remote locations. The computing systems for drones are becoming a new venue for research in cyber-physical systems. Autonomous drones require integrated intelligent decision systems to control and manage their flight missions in the absence of human operators. One of the most crucial aspects of drone mission control and management is related to the optimization of battery lifetime. Typical drones are powered by on-board batteries, with limited capacity. But drones are expected to carry out long missions. Thus, a fully automated management system that can optimize the operations of battery-operated autonomous drones to extend their operation time is highly desirable. This paper presents several contributions to automated management systems for battery-operated drones: (1) We conduct empirical studies to model the battery performance of drones, considering various flight scenarios. (2) We study a joint problem of flight mission planning and recharging optimization for drones with an objective to complete a tour mission for a set of sites of interest in the shortest time. This problem captures diverse applications of delivery and remote operations by drones. (3) We present algorithms for solving the problem of flight mission planning and recharging optimization. We implemented our algorithms in a drone management system, which supports real-time flight path tracking and re-computation in dynamic environments. We evaluated the results of our algorithms using data from empirical studies. (4) To allow fully autonomous recharging of drones, we also develop a robotic charging system prototype that can recharge drones autonomously by our drone management system