Automated Analysis and Optimization of Distributed Self-Stabilizing Algorithms

Self-stabilization [2] is a versatile technique for recovery from erroneous behavior due to transient faults or wrong initialization. A system is self-stabilizing if (1) starting from an arbitrary initial state it can automatically reach a set of legitimate states in a finite number of steps and (2) it remains in legitimate states in the absence of faults. Weak-stabilization [3] and probabilistic-stabilization [4] were later introduced in the literature to deal with resource consumption of self-stabilizing algorithms and impossibility results. Since the system perturbed by fault may deviate from correct behavior for a finite amount of time, it is paramount to minimize this time as much as possible, especially in the domain of robotics and networking. This type of fault tolerance is called non-masking because the faulty behavior is not completely masked from the user [1]. Designing correct stabilizing algorithms can be tedious. Designing such algorithms that satisfy certain average recovery time constraints (e.g., for performance guarantees) adds further complications to this process. Therefore, developing an automatic technique that takes as input the specification of the desired system, and synthesizes as output a stabilizing algorithm with minimum (or other upper bound) average recovery time is useful and challenging. In this thesis, our main focus is on designing automated techniques to optimize the average recovery time of stabilizing systems using model checking and synthesis techniques. First, we prove that synthesizing weak-stabilizing distributed programs from scratch and repairing stabilizing algorithms with average recovery time constraints are NP-complete in the state-space of the program. To cope with this complexity, we propose a polynomial-time heuristic that compared to existing stabilizing algorithms, provides lower average recovery time for many of our case studies. Second, we study the problem of fine tuning of probabilistic-stabilizing systems to improve their performance. We take advantage of the two properties of self-stabilizing algorithms to model them as absorbing discrete-time Markov chains. This will reduce the computation of average recovery time to finding the weighted sum of elements in the inverse of a matrix. Finally, we study the impact of scheduling policies on recovery time of stabilizing systems. We, in particular, propose a method to augment self-stabilizing programs with k-central and k-bounded schedulers to study dierent factors, such as geographical distance of processes and the achievable level of parallelism

Resilience analysis of offshore safety and power system

Harsh and deep waters create challenging environments for offshore drilling and production facilities, resulting in increased chances of failure. This necessitates improving the resilience of the engineering system, which is the capability of a system to recover its functionality during disturbance and failure. The present work proposes an approach to quantify resilience as a function of vulnerability and maintainability. The approach assesses proactive and reactive defense mechanisms along with operational factors to respond to unwanted disturbances and failures. The proposed approach employs a Bayesian network to build two resilience models. Two developed models are applied to: 1) a hydrocarbon release scenario during an offloading operation in a remote and harsh environment, and 2) the main requirements to improve the resilience of an offshore power management system. This study attempts to relate resilience capacity of a system to the system’s absorptive, adaptive and restorative capacities. These capacities influence pre-disaster and post-disaster strategies that can be mapped to enhance resilience of the system. Furthermore, the technique of an object-oriented framework is adopted to better structure the resilience model as a function of a system’s adaptability, absorptive and restorative capabilities. Sensitivity analysis is also conducted to analyze the impact and interdependencies among different variables to enhance resilience

Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics

Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural networks. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network (PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a large-deformable beam is given as an example.Comment: 275 pages, 158 figures. Appeared online on 2023.03.01 at CMES-Computer Modeling in Engineering & Science