On top of machine learning (ML) models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage (case study 1) and the remaining useful life prediction of turbofan engines (case study 2).

In recent years, multi-agent deep reinforcement learning has progressed rapidly as reflected by its increasing adoptions in industrial applications. This paper proposes a Guided Probabilistic Reinforcement Learning (Guided-PRL) model to tackle maintenance scheduling of multi-component systems in the presence of uncertainty with the goal of minimizing the overall life-cycle cost. The proposed Guided-PRL is deeply rooted in the Actor-Critic (AC) scheme. Since traditional AC falls short in sampling efficiency and suffers from getting stuck in local minima in the context of multi-agent reinforcement learning, it is thus challenging for the actor network to converge to a solution of desirable quality even when the critic network is properly configured. To address these issues, we develop a generic framework to facilitate effective training of the actor network, and the framework consists of environmental reward modeling, degradation formulation, state representation, and policy optimization. The convergence speed of the actor network is significantly improved with a guided sampling scheme for environment exploration by exploiting rules-based domain expert policies. To handle data scarcity, the environmental modeling and policy optimization are approximated with Bayesian models for effective uncertainty quantification. The Guided-PRL model is evaluated using the simulations of a 12-component system as well as GE90 and CFM56 engines. Compared with four alternative deep reinforcement learning schemes, the Guided-PRL lowers life-cycle cost by 34.92% to 88.07%. In comparison with rules-based expert policies, the Guided-PRL decreases the life-cycle cost by 23.26% to 51.36%.

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared.

In this paper, we develop a generic physics-informed neural network (PINN)-based framework to assess the reliability of multi-state systems (MSSs). The proposed framework follows a two-step procedure. In the first step, we recast the reliability assessment of MSS as a machine learning problem using the framework of PINN. A feedforward neural network with two individual loss groups is constructed to encode the initial condition and the state transitions governed by ordinary differential equations in MSS, respectively. Next, we tackle the problem of high imbalance in the magnitudes of back-propagated gradients from a multi-task learning perspective and establish a continuous latent function for system reliability assessment. Particularly, we regard each element of the loss function as an individual learning task and project a task’s gradient onto the norm plane of any other task with a conflicting gradient by taking the projecting conflicting gradients (PCGrad) method. We demonstrate the applications of the proposed framework for MSS reliability assessment in a variety of scenarios, including time-independent or dependent state transitions, where system scales increase from small to medium. The computational results indicate that PINN-based framework reveals a promising performance in MSS reliability assessment and incorporation of PCGrad into PINN substantially improves the solution quality and convergence speed of the algorithm.

Teams formulated by aviation professionals are essential in maintaining a safe and efficient aerodrome environment. Nonetheless, the shared situational awareness between the flight crews under adverse weather conditions might be impaired. This research aims to evaluate the impact of a proposed enhancement in communication protocol on cognitive workload and develop a human-centred classification model to identify hazardous meteorological conditions. Thirty groups of subjects completed four post-landing taxiing tasks under two visibility conditions (CAVOK/CAT IIIA) while two different communication protocols (presence/absence of turning direction information) were adopted by the air traffic control officer (ATCOs). Electroencephalography (EEG) and the NASA Task Load Index were respectively used to reflect the pilot’s mental state and to evaluate the pilot’s mental workload subjectively. Results indicated that impaired visibility increases the subjective workload significantly, while the inclusion of turning direction information in the ATCO’s instruction would not significantly intensify their cognitive workload. Mutual information was used to quantitatively assess the shared situational awareness between the pilot flying and the pilot monitoring. Finally, this research proposes a humancentred approach to identify potentially hazardous weather conditions from EEG power spectral densities with Bayesian neural networks (BNN). The classification model has outperformed other baseline algorithms with an accuracy of 66.5%, an F1 score of 61.4%, and an area under the ROC of 0.749. Using the concept of explainable AI with Shapley Additive Explanations (SHAP) values, the exploration of latent mental patterns formulates novel knowledge to gain insights into the vital physiological indicators of the pilots in response to different scenarios from the BNN model. In the long term, the model facilitates the decision regarding the necessity of providing automation and decision-making aids to pilots.