In system reliability assessment, expert opinions are oftentimes elicited to cope with the issue of poor quantity of failure data. However, information from expert subjective judgments may exhibit imprecision and be elicited from multiple physical levels of a system. Moreover, the elicited information may be conflicting as experts own varying backgrounds of knowledge as well as differentiated cognitive levels, which, thereby, cannot reach a consistent reliability estimate. In this article, we aim at conducting the reliability assessment of multistate systems by fusing conflicting multisource imprecise information (MSII) from the consensus reaching perspective. We utilize an aggregation operator to fuse individual opinions into a collective opinion in the form of mass functions. Evidence distance is, then, adopted to quantify the dissimilarity between individual and collective opinions, and accordingly, a measurement of the average degree of consensus is proposed. In this way, the consensus reaching model is formulated by minimizing the total calibration of MSII with the constraint of a predetermined consensus threshold. The consensus reaching model is resolved by a feasibility-based particle swarm optimization algorithm. A numerical example, along with an application of control rod drive mechanism in nuclear reactors, is used for the demonstration of the effectiveness of the proposed method.

In the system reliability assessment by multisource information fusion, the various sources of information often display biases and may be conflicting with each other. Practical scenarios typically require a consensus on the reliability estimate, which indicates that the multisource information has to be properly refined. This study introduces a consensus-reaching process aiming at calibrating imprecise information from diverse experts' opinions for multistate systems. Specifically, two interactive consensus reaching models, i.e., interactive minimum-cost reliability consensus model and interactive maximum consensus degree model, are put forth to allow experts to make cost-effective preference modifications to reach a reliability consensus. The interactive consensus reaching models use the evidential network and evidential utility function to amalgamate multisource imprecise information to reach a nominal reliability consensus. A feedback mechanism based on the belief Jensen–Shannon divergence measure is, therefore, developed to foster interaction between the expert's imprecise information and the nominal reliability consensus. Through the interactive consensus reaching process, the unified reliability estimate is assessed via a feasibility-based particle swarm optimization. The effectiveness of the proposed method is demonstrated via a numerical example and a control rod drive mechanism in nuclear power plants.

Power substations are widely used as crucial components of power grids but also exposed to a high risk of earthquakes. Enhancing the resilience of power substations plays an important role for power grids to resist earthquakes. However, the uncertainty of equipment failure has posed a significant obstacle to enhancing resilience. In this article, considering the equipment hardening strategy for the power substation, a two-stage distributionally robust optimization model is put forth for earthquake resilience enhancement of the power substations. The optimal equipment hardening strategy is determined prior to an earthquake, and the recovery sequence of the damaged equipment is optimized after the earthquake to enhance the resilience of the power substation. A decision-dependent moment-based ambiguity set is constructed to model the impact of the hardening strategy on the uncertain failure probability of equipment. A customized nested column-and-constraint generation algorithm (NC&CG) is put forth to solve the optimization model. To improve the computational efficiency, we propose a novel heuristic algorithm to solve the main problem of the inner NC&CG according to the power substation structure. The proposed method is demonstrated in the case of a simplified 220 kV power substation. The results show that the distributionally robust approach can effectively enhance the earthquake resilience of power infrastructure under uncertainty of equipment failure. The value of implementing an effective algorithm to quickly obtain the optimal solution in large-scale problems is also highlighted.

Defect detection tasks of solid propellants (SPs), involving size, shape, and surface defects, are essential for ensuring the quality of many industrial products. Developing separate models for three tasks, however, is complicated and inefficient due to the redundant deployment. Multitask learning (MTL), with its potential for knowledge sharing, may greatly reduce the space and power consumption, but still faces the challenges of destructive interference and empirical tradeoffs between tasks. To this end, a novel end-to-end network for multidefect detection of SPs is put forth: 1) a new setting for MTL without any empirical tradeoffs is introduced, in which the knowledge is shared while the models are not visible to each other among diverse tasks; 2) in this setting, a bilateral feature extractor is constructed to extract both low- and high-level features, and a feature fusion module is further exploited to encourage each task to adaptively learn the task-specific knowledge; 3) an end-to-end training manner with a dynamic balance strategy and a gradient stop-flow strategy is designed to ensure that different tasks can benefit from, but do not interfere with, each other; 4) the introduction of semantic knowledge from the size detection branch enables the surface detection branch to learn semantic features beyond only pixel-to-pixel mapping. A smoothness construction loss is further designed to boost the performance of the surface detection task. Experimental results on an image dataset from a real-world manufacturing line show that the setting for MTL has the superiority in terms of the model size, inference speed, and detection accuracy.

Deep learning methods have received tremendous attention in remaining useful life (RUL) prediction in recent years. Despite the promising results achieved by those deep learning methods, they failed to take account of the impact of varying future operations on RUL prediction and prognostics uncertainty. In most industrial scenarios, the RUL of products is closely related to future missions and loading profiles, and they ought to be considered for RUL prediction. In addition, Bayesian deep learning treats the model parameters as random variables, and takes advantage of the Bayesian formulas for adaptive model parameter updating to obtain credible intervals of RUL prediction. In this article, a Bayesian dual-input-channel long short-term memory (BDIC-LSTM) network is put forth to conduct the point estimation and credible interval estimation of RUL prediction. The BDIC-LSTM network consists of a DIC-LSTM network and an improved Monte Carlo dropout (IMCD) method to effectively extract the features of future operations and quantify the prognostics uncertainty, respectively. In the DIC-LSTM network, the raw signal data are fed into the main input channel consisting of LSTM modules. Meanwhile, bidirectional LSTM (Bi-LSTM) modules are leveraged as an auxiliary input channel to fully extract the future operation information in the operation data. The IMCD method is investigated to estimate the credible intervals of RUL via decomposing the prognostics uncertainty into aleatory uncertainty of measurement data and epistemic uncertainty of the network. For the training of the BDIC-LSTM network, a padding and packing training mode, an improved loss function, together with a Lookahead optimizer, are devised to accelerate the convergence speed and enhance the accuracy of prognostics. Experiments on the C-MAPSS dataset are carried out to validate the effectiveness of the proposed method.

Inspection is a crucial activity for an engineered system as its results can reduce the uncertainty of identifying the true states of the system and its components, so as to facilitate subsequent proactive maintenance. The preliminary work to conduct an inspection activity is to evaluate its effectiveness. In many real-world scenarios, engineered systems oftentimes possess both multistate and hierarchical characteristics, and inspection can be performed across multiple physical levels of a system. We, therefore, need a measure to assess the effectiveness of a multilevel inspection activity of multistate systems. Inspired by the concept of importance measure, in this article, we define a new measure, namely, inspection importance measure (InsIM), to assess the contribution of a multilevel inspection strategy to the efficiency improvement of the subsequent preventive maintenance from a value of information perspective. The proposed measure evaluates the increased efficiency of preventive maintenance after conducting multilevel inspection activities. The procedure of the proposed InsIM contains four steps: 1) calculating the efficiency of the optimal maintenance policy identified without inspections, 2) updating the system's state distribution by multilevel inspection activities, 3) calculating the efficiency of the optimal maintenance policy identified with inspections, and 4) evaluating the expected improvement of maintenance policy. A five-component system and a real-world programmable logic controller control system are exemplified to demonstrate the accuracy and effectiveness of the proposed method. The results indicate that the InsIM can significantly enhance the efficiency of the subsequent proactive maintenance decision.

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

Fast recognition of integrated circuit (IC) markings is an essential but challenging task in electronic device manufacturing lines. This article develops an adaptive deep learning framework to facilitate the fast marking recognition of IC chips. The proposed framework contains four deep learning components, namely, chip segmentation, orientation correction, character extraction, and character recognition. The four components utilize different convolutional neural network structures to guarantee excellent adaptivity to a wide range of IC types and mitigate the influence of the low-quality chip images. In particular, the character extraction model is comprised of two improved label generation strategies and a proposed border correction method, so as to accommodate tiny scale chips and compactly printed markings. Experiments from the chip image dataset of a real laptop manufacturing line reached a recognition Precision of 91.73% and the Recall of 92.93%. The results demonstrate the superiority of the proposed framework to the state-of-the-art models and the effectiveness of handling a great diversity of chips with different scales, shapes, text fonts, marking colors, and layouts.

As multistate system (MSS) reliability models can characterize the multistate deteriorating nature of engineering systems, they have received considerable attention in the past decade. The states of a multistate system/component can be distinguished by its performance capacity, which deteriorates over time and can be restored by maintenance activities. On the other hand, the deterioration of a system/component is, oftentimes, controllable by setting a loading strategy. In this article, a dynamic load optimization problem for repairable MSSs is investigated to achieve the maximum expected cumulative performance within a finite time horizon and limited maintenance resources. The degraded components in a system are dynamically maintained to recover to their better conditions, whereas the performance rate of each component can also be dynamically specified. The resulting sequential decision problem is formulated as a Markov decision process with a continuous action space and a mixed integer discrete continuous state space. The deep deterministic policy gradient algorithm, which is a specific deep reinforcement learning algorithm in the actor−critic framework, is customized to overcome the “curse of dimensionality” and mitigate the uncountable state and action spaces. The effectiveness of the proposed method is examined by two illustrative examples, and a set of comparative studies are conducted to demonstrate the advantage of the proposed dynamic loading strategy.

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

Improving reliability and eliminating the potential design risk are crucial for product design. Failure mode and effect analysis (FMEA), as an effective reliability assurance tool, has been extensively used in product design. However, causalities among failure modes, interactions among risk factors, and correlations among risk evaluations were not jointly considered in existing FMEA methods. On the other hand, the cost and time caused by the occurrence of failure modes were seldom incorporated into risk factors. Due to the lack of accurate values and/or information loss of customers and experts, these risk factors inevitably contain uncertainty that cannot be overlooked in product design. In this article, a novel FMEA-based approach is proposed to facilitate risk analysis of product design under uncertainty. In this approach, the stable grey causality vector state and the grey interaction vector are respectively established to characterize causalities and interactions. To reduce the uncertainty contained in cost and time, the extended information axiom is put forth, and then, their grey information contents can be obtained and are to be incorporated into the design. Subsequently, we extend Choquet integral to prioritize the potential failure modes and identify the optimal design scheme while coping with correlations. The proposed approach is validated by an example of a substrate design.

In this article, we develop a mixture of Gaussians-evidential hidden Markov model (MoG-EHMM) to fuse expert knowledge and condition monitoring information for remaining useful life (RUL) prediction under the belief function theory framework. The evidential expectation-maximization algorithm is implemented in the offline phase to train the MoG-EHMM based on historical data. In the online phase, the trained model is used to recursively update the health state and reliability of a particular individual system. The predicted RUL is, then, represented in the form of its probability mass function. A numerical metric is defined based on the Bhattacharyya distance to measure the RUL prediction accuracy of the developed methods. We applied the developed methods on a simulation experiment and a real-world dataset from a bearing degradation test. The results demonstrate that despite imprecisions in expert knowledge, the performance of RUL prediction can be substantially improved by fusing expert knowledge with condition monitoring information.

The reliability function of a specific individual system can be dynamically updated by utilizing inspection data collected over time. However, due to limited inspection resources, such as time, budget, and manpower, it is oftentimes impossible to collect all the inspection data for all the components, subsystems, and the entire system simultaneously. There is an urgent need to optimally allot the limited inspection resources across multiple physical levels of a system, so as to identify the health status of a system and/or its subset of components of interest as accurately as possible to facilitate the ensuing system health management. To address the above research question, a metric is put forth in this paper to quantify the effectiveness of a particular multilevel inspection strategy for multistate systems (MSSs). Based on the proposed metric, an optimization problem is formulated to seek the optimal multilevel inspection strategy which possesses the maximum effectiveness of revealing the true state of a system and/or its subset of components of interest under limited inspection resources. The resulting optimization problem is resolved by a tailored ant colony optimization algorithm. The findings from our illustrative examples are 1) the proposed metric is capable of quantifying the effectiveness of various multilevel inspection strategies; 2) the analytical solution of the proposed metric is exactly the same with the simulation results, but much more computationally efficient; and 3) the optimal inspection strategy varies with respect to the operation time of a specific individual system.