Battery degradation modeling in the presence of uncertainty is a key but challenging issue in the application of battery predictive maintenance. This article develops a capacity prediction model with uncertainty quantification for lithium-ion batteries and proposes a dynamic maintenance strategy that can help to make an optimized decision at each battery cycle stage. To be specific, after using the 1-D convolution neural network (1dCNN), deep representative features hidden in original measured signals are extracted. Then, the bidirectional long short-term memory (Bi-LSTM) is applied to estimate the battery capacities, while the quantile regression (QR) layer is embedded into the construction of the Bi-LSTM network to obtain the capacities for different quantiles. Next, the kernel density estimation (KDE) is utilized to derive the probability density of the predicted points at each battery cycle stage. Thus, the combination of 1dCNN, Bi-LSTM, QR, and KDE, named 1dCNN-BiLSTMQR-KDE, forms an efficacious capacity prediction model with reliable uncertainty management. Finally, the costs of different decisions at each battery cycle stage are evaluated, and the decision with the lower cost will be chosen. The whole proposition is verified on battery degradation datasets from NASA, and the comparison with other methods show that the proposed method is competitive.

Reliable and accurate aeroengine remaining useful life (RUL) prediction plays a key role in the aeroengine prognostics and health management (PHM) system. However, due to the epistemic uncertainties associated with aeroengine systems, prediction errors are unavoidable and sometimes significant in traditional deterministic point prediction methods. To improve the accuracy and credibility of RUL prediction, a novel prediction interval (PI) estimation method is proposed to quantify the uncertainties in RUL prediction. The proposed method involves data clustering, mathematical–statistical analysis, and deep learning techniques and is achieved through off-line and online phases. In the off-line phase, an enhanced fuzzy c-means (FCM) algorithm is proposed to divide the aeroengine health status into several discrete states. After labeling the health state of each sampling point, PIs are computed for them. This step is achieved by the empirical distributions of errors associated with all instances belonging to the health state under consideration. In the online phase, a bidirectional long short-term memory (Bi-LSTM) network is employed to estimate the boundaries of point prediction, and thus, the PI of aeroengine RUL is generated. The aeroengine degradation dataset from NASA is used to validate the proposed RUL PI estimation method. The results obtained indicate that the proposed method is a promising tool for providing reliable aeroengine RUL interval estimates, which can inform maintenance-related decisions.

Modern engineering systems are usually equipped with a variety of sensors to measure real-time operating conditions. Based on the condition monitoring data from multiple sensor sources, this paper deals with a dynamic predictive maintenance scheduling using deep learning ensemble for system health prognostics. The deep learning ensemble model is composed of deep autoencoder and bidirectional long short-term memory in series, and aims to accurately estimate the system health state and remaining useful life. The deep autoencoder is used to extract the deep representative features hidden in condition monitoring data, whereas the inclusion of the bidirectional long short-term memory allows learning the temporal correlation information of features in both forward and backward time directions. Thus, the combination of the two models forms an effective model. With obtained prognostic information, optimal maintenance decisions are determined by two designed rules. The first rule presets a reliable remaining useful life threshold to dynamically judge whether maintenance is carried out at current inspection time, while the second one selects a degradation state to dynamically determine whether to place a spare part order. The performance of the proposed dynamic predictive maintenance strategy is measured by the maintenance cost per unit operating time (cost rate) using the aero-engine dataset from NASA. Its effectiveness is demonstrated by comparing with recent publications.

Interval estimation of landslide displacement prediction is crucial for the landslide early warning. To improve the accuracy of landslide displacement prediction, a dynamic prediction model based on double moving average (DMA) method and long short-term memory (LSTM) network is proposed. The DMA method is used to decompose the cumulative displacement of landslide into trend and periodic displacements, while the LSTM network is used to predict the trend and periodic displacements. The predicted values of cumulative displacement are obtained by reconstructing the predicted trend and periodic displacements. To quantify the uncertainties associated with the predicted values, the prediction intervals are derived according to the probability estimation theory. The proposed interval estimation method was validated on the Baishuihe landslide in the Three Gorges Reservoir area of China. The results show that the LSTM network performs better than the support vector machine (SVM) and Elman network, while the DMA decomposition method outperforms the single moving average (SMA) method. Besides, the proposed estimation method can construct high-quality prediction intervals.

Failure prediction and maintenance decision-making are two core activities in a prognostics and health management (PHM) system. However, they are often studied independently and hierarchically. The main goal of this paper is to combine system failure prediction with maintenance decision-making to develop a predictive maintenance strategy. System failure prediction is achieved by constructing an ensemble model of deep autoencoder (DAE), long short-term memory (LSTM), quantile regression (QR) and kernel density estimation (KDE), namely DAE-LSTMQR-KDE. Then, on the basis of the probability density of system failure time obtained from the ensemble model, replacement cost function (RCF) and ordering cost function (OCF) are proposed to support maintenance and inventory decisions. Finally, optimal decisions are determined by minimizing the two cost functions. A score equal to 246.59 and a coverage width-based criterion (CWC) index equal to 0.35 were obtained when the DAE-LSTMQR-KDE ensemble model was applied to C-MAPSS dataset, while the average maintenance cost rate (MCR) of the proposed maintenance strategy was 0.74. The results demonstrated that the proposed prediction and maintenance method outperforms several state-of-the-art methods. In addition, different cost structure scenarios are also investigated to illustrate the flexibility of maintenance decisions based on failure prediction information.

In recent decades, landslide displacement forecasting has received increasing attention due to its ability to reduce landslide hazards. To improve the forecast accuracy of landslide displacement, a dynamic forecasting model based on variational mode decomposition (VMD) and a stack long short-term memory network (SLSTM) is proposed. VMD is used to decompose landslide displacement into different displacement subsequences, and the SLSTM network is used to forecast each displacement subsequence. Then, the forecast values of landslide displacement are obtained by reconstructing the forecast values of all displacement subsequences. On the other hand, the SLSTM networks are updated by adding the forecast values into the training set, realizing the dynamic displacement forecasting. The proposed model was verified on the Dashuitian landslide in China. The results show that compared with the two advanced forecasting models, long short-term memory (LSTM) network, and empirical mode decomposition (EMD)–LSTM network, the proposed model has higher forecast accuracy.