Tabular data is the most widely used data form in real-world applications, and tree-based models are suitable for it due to their model structures. In practice, it is crucial to quantify predictive uncertainty, and several uncertainty estimation methods have been developed for tree-based models. However, some of them compromise point estimation accuracy or incur high computational overhead. To address this limitation, we propose a variance-based method for predictive uncertainty estimation of tabular data using gradient boosting decision tree (VarBoost). VarBoost estimates variance by analytically calculating statistical characteristics based on gradient boosting strategy, ensuring efficient and accurate variance estimation while maintaining point estimation performance. To avoid overfitting or underfitting, hyperparameters are determined via cross-validation using proper scoring rules that balance calibration and sharpness. The effectiveness of VarBoost is validated by comparisons with several state-of-the-art uncertainty estimation methods on a collection of UCI tabular datasets. Experimental results demonstrate that VarBoost achieves superior performance in both point estimation and uncertainty estimation.

Concept drift presents significant challenge in many real-world data stream regression tasks, particularly in industrial applications. This challenge becomes even more complex when concept drift is accompanied by data imbalance. To address this issue, we propose an uncertainty-driven online deep ensemble framework (UODEF) which leverages deep ensemble embedding with dynamic weight adjustment based on both performance and time factor. Specifically, UODEF incorporates epistemic uncertainty-driven drift detection to detect concept drift, and retrains new base learners utilizing historical information to effectively handle recurring drifts. To address data imbalance, an uncertainty-driven adaptive oversampling technique is developed to dynamically identify and oversample rare samples, ensuring that new base learners are unbiased. Experiments on a real-world dataset from a diesel hydrofining process, collected in a petrochemical workshop, demonstrate that UODEF outperforms three recently proposed methods for imbalanced drifting data stream regression.

The wheels are among the most critical components which largely influence the safe operation of high-speed trains. The existing research in reliability modeling typically assumes the wheel degradation to be a one-dimensional degradation process. This could incur a deficiency in practice, as the wheel degradation is in fact the superposition of multiple complex degradation processes, involving wheel tread wear and wheel polygonal wear. Random shocks also contribute to the wheel degradation. Moreover, these processes are correlated with each other. To fully consider these factors, this article proposes a multistate model for multidimensional degradations. The piecewise-deterministic Markov process (PDMP) model is applied to describe the mutual dependencies between random shocks and multiple degradations. Conventionally, the parameters of PDMP are set by experts’ experience. This article investigates maximum likelihood estimation to estimate the model parameters. Finally, the Monte Carlo simulation algorithm is proposed to evaluate the high-speed train wheel's reliability. Numerical experiments were conducted to validate the proposed method on high-speed train wheels subject to tread wear, polygonal wear, and wheel-rail impacts, which show that dependencies among multidimensional degradation processes and random shocks will largely affect the reliability of the wheels. The application to high-speed train wheels shows the effectiveness of the proposed model.

Fault diagnosis plays an important role in guiding maintenance actions and prevent safety hazards. With the development of sensor and computer technology, deep learning (DL)-based fault diagnosis methods have been substantially developed. However, the inability to reliably represent and quantify uncertainties associated with the diagnostic results greatly hinders their industrial applicability. In this article, an uncertainty-aware fault diagnosis framework based on the Bayesian DL is proposed considering uncertainty quantification and calibration. To achieve explainable representations of different types of uncertainties, aleatoric uncertainty, epistemic uncertainty, and distributional uncertainty, which stem from the noise inherent in the observations, lack of knowledge, and domain shift, respectively, are jointly characterized for uncertainty quantification. Besides, to improve the quantification accuracy and obtain trustworthy diagnostic results to support subsequent maintenance, a novel calibration loss is proposed for the uncertainty calibration. The proposed method is applied to the two different bearing datasets to demonstrate its effectiveness in providing both the accurate diagnostic results and calibrated uncertainty quantification.

In this article, deep learning (DL) has attracted increasing attention for remaining useful life (RUL) prediction. However, most DL-based prognostics methods only provide deterministic RUL values while ignoring the associated epistemic and aleatoric uncertainties. In practice, it is important to know the exact confidence in model predictions for decision making. In this article, a Bayesian deep learning (BDL) framework for RUL prediction incorporating uncertainty quantification and calibration is proposed. First, the epistemic and aleatoric uncertainties, which account for the ignorance about the model and the noise inherent in the observations, respectively, are characterized by integrating both types of uncertainties into a BDL framework. Second, to avoid under- and over-confident predictions, a novel iterative calibration method is proposed to jointly calibrate epistemic, aleatoric, and predictive uncertainties by combining isotonic regression with standard deviation scaling. The effectiveness of the proposed method is demonstrated by the case study of turbofan engines and lithium-ion batteries datasets.

A modeling and optimization framework for the maintenance of systems under epistemic uncertainty is presented in this paper. The component degradation processes, the condition-based preventive maintenance, and the corrective maintenance are described through piecewise-deterministic Markov processes in consideration of degradation dependence among degradation processes. Epistemic uncertainty associated with component degradation processes is treated by considering interval-valued parameters. This leads to the formulation of a multi-objective optimization problem whose objectives are the lower and upper bounds of the expected maintenance cost, and whose decision variables are the periods of inspections and the thresholds for preventive maintenance. A solution method to derive the optimal maintenance policy is proposed by combining finite-volume scheme for calculation, differential evolution, and nondominated sorting differential evolution for optimization. An industrial case study is presented to illustrate the proposed methodology.

Standby techniques of different types have been applied in a wide range of industries to improve system reliability. Since the reliabilities of the operating components are generally high in the initial period of the mission and the standby components are hardly needed, it is more reasonable to set a standby component into cold standby state at the beginning and switch it into the warm standby state after certain period. In this paper, we consider 1-out-of-N: G standby systems with components whose lifetimes can follow general distributions and investigate the optimal state transfer scheduling problem with the objective of maximizing system reliability at mission time. For system reliability evaluation, the system reliability functions are derived in a recursive way and the numerical methods based on the closed Newton-Cotes quadrature rules are proposed without using derivatives. The optimal state transfer scheduling is derived by using the meta-heuristic differential evolution algorithm. By identifying the optimal state transfer scheduling, the state transfer order of standby components can also be determined. Two numerical examples are provided to illustrate the proposed methodology and demonstrate its effectiveness.

Component importance measures (IMs) are widely used to rank the importance of different components within a system and guide allocation of resources. The criticality of a component may vary over time, under the influence of multiple dependent competing degradation processes and maintenance tasks. Neglecting this may lead to inaccurate estimation of the component IMs and inefficient related decisions (e.g., maintenance, replacement, etc.). The work presented in this paper addresses the issue by extending the mean absolute deviation IM by taking into account: 1) the dependency of multiple degradation processes within one component and among different components; 2) discrete and continuous degradation processes; and 3) two types of maintenance tasks: condition-based preventive maintenance via periodic inspections and corrective maintenance. Piecewise-deterministic Markov processes are employed to describe the stochastic process of degradation of the component under these factors. A method for the quantification of the component IM is developed based on the finite-volume approach. A case study on one section of the residual heat removal system of a nuclear power plant is considered as an example for numerical quantification.

Components are often subject to multiple competing degradation processes. This paper presents a reliability assessment framework for multicomponent systems whose component degradation processes are modeled by multistate and physics-based models with limited statistical degradation/failure data. The piecewise-deterministic Markov process modeling approach is employed to treat dependencies between the degradation processes within one component or/and among components. A computational method combining binary decision diagrams (BDDs) and Monte Carlo simulation (MCS) is developed to solve the model. A BDD is used to encode the fault tree of the system and obtain all the paths leading to system failure or operation. MCS is used to generate random realizations of the model and compute the system reliability. A case study is presented, with reference to one branch of the residual heat removal system of a nuclear power plant.

Components are often subject to multiple competing degradation processes. For multicomponent systems, the degradation dependence within one component or/and among components need to be considered. Physics-based models and multistate models are often used for component degradation processes, particularly when statistical data are limited. In this paper, we treat dependence between degradation processes within a piecewise-deterministic Markov process (PDMP) modeling framework. Epistemic (subjective) uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters, to take this into account, we describe the parameters of the PDMP model as fuzzy numbers. Then, we extend the finite-volume method to quantify the (fuzzy) reliability of the system. The proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant, and a comparison is offered with a Monte Carlo simulation solution the results show that our method can be most efficient.

We extend a multi-state physics model (MSPM) framework for component reliability assessment by including semi-Markov and random shock processes. Two mutually exclusive types of random shocks are considered: extreme, and cumulative. Extreme shocks lead the component to immediate failure, whereas cumulative shocks simply affect the component degradation rates. General dependences between the degradation and the two types of random shocks are considered. A Monte Carlo simulation algorithm is implemented to compute component state probabilities. An illustrative example is presented, and a sensitivity analysis is conducted on the model parameters. The results show that our extended model is able to characterize the influences of different types of random shocks onto the component state probabilities and the reliability estimates.

Multistate physics modeling (MSPM) of degradation processes is an approach proposed for estimating the failure probability of components and systems. This approach integrates multistate modeling, which describes the degradation process through transitions among discrete states (e.g., initial, microcrack, rupture, etc.), and physics modeling by (physics) equations that describe the degradation process within the states. In reality, the degradation process is non-Markovian, its transition rates are time-dependent, and the degradation is possibly influenced by uncertain external factors such as temperature and stress. Under these conditions, it is in general difficult to derive the state probabilities analytically. In this paper, we overcome this difficulty by building a simulation model supported by a stochastic Petri net representing the multistate degradation process. The proposed modeling approach is applied to the problem of a nuclear component undergoing stress corrosion cracking. The results are compared with those derived from the state-space enrichment Markov chain approximation method applied in a previous work of literature.