Commercial Modular Aero-Propulsion System Simulation Research Articles

Using transformer and a reweighting technique to develop a remaining useful life estimation method for turbofan engines

Estimating the Remaining Useful Life (RUL) of industrial machinery is an important task in Prognostics and Health Management (PHM). Accurate RUL prediction based on current health status and real-time sensor measurements can help establish efficient maintenance strategies in advance, thus improving the productivity and efficiency of machinery operations. However, considering the nature of industrial machinery, a data imbalance problem, which exists in current RUL estimation datasets like the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset, hinders data-driven approaches. To address the detrimental data imbalance problem and improve estimation performance, this research proposes an Adaptive RUL-wise Reweighting (ARR) technique. ARR uses kernel smoothing to maintain the inherent continuity of RUL and a reweighting method to rebalance the effects of samples with different ground-truth RULs. In addition, this research proposes a novel RUL estimation method that uses a transformer architecture, which has not yet been widely applied for PHM tasks. Using a transformer-based estimation model with high expressive power capable of handling multivariate time-series data has proven effective in RUL estimation. Comprehensive experiments using the C-MAPSS dataset based on cross validation are conducted to find optimal hyperparameter configurations and to validate the proposed method’s effectiveness in RUL estimation. For subsets FD001 and FD003 of the C-MAPSS dataset, the proposed method provides state-of-the-art estimation performance with the lowest Root Mean Squared Error (RMSE) values of 11.36 and 11.28 and score values of 192.22 and 133.41, respectively. The proposed method also shows highly competitive performance on subsets FD002 and FD004 of the C-MAPSS dataset.

Remaining Useful Life Prediction for Aircraft Engines under High-Pressure Compressor Degradation Faults Based on FC-AMSLSTM

The healthy operation of aircraft engines is crucial for flight safety, and accurate Remaining Useful Life prediction is one of the core technologies involved in aircraft engine prognosis and health management. In recent years, deep learning-based predictive methods within data-driven approaches have shown promising performance. However, for engines experiencing a single fault, such as a High-Pressure Compressor fault, existing deep learning-based predictive methods often face accuracy challenges due to the coupling relationship between different fault modes in the training dataset that includes a mixture of multiple fault modes. In this paper, we propose the FC-AMSLSTM method, a novel approach for Remaining Useful Life prediction specifically targeting High-Pressure Compressor degradation faults. The proposed method effectively addresses the limitations of previous approaches by fault classification and decoupling fault modes from multiple operating conditions using a decline index. Then, attention mechanisms and multi-scale convolutional neural networks are employed to extract spatiotemporal features. The long short-term memory network is then utilized to model RUL estimation. The experiments are conducted using the Commercial Modular Aero-Propulsion System Simulation dataset provided by NASA. The results demonstrate that compared to other prediction models, the FC-AMSLSTM method effectively reduces RUL prediction error for HPC degradation faults under multiple operating conditions.

A regularized constrained two-stream convolution augmented Transformer for aircraft engine remaining useful life prediction

Remaining Useful Life (RUL) prediction is of great significance for maintaining the reliability and safety of industrial equipment. To address the challenges faced by existing methods in simultaneously extracting local and global degradation information from monitoring data. This paper proposes a Two-Stream Convolution Augmented Transformer (TACT) model based on L2 regularization constraint. Specifically, we design the parallel multi-scale Convolution Neural Network (CNN) and Transformer module to combine the local modeling ability of CNN and the global modeling ability of Transformer to improve the overall architecture of RUL prediction model. Moreover, the two-stream network based on the parallel structure also realizes the synchronous extraction of different time steps and sensor features in the sequence. Then, in the process of model training, the prediction reliability constraint is fused, the delay prediction constraint term is introduced, and the L2 regularization loss function is constructed. Finally, extensive experiments on the commercial modular aero-propulsion system simulation (C-MAPSS) show that our model provides competitive performance in terms of Root-Mean-Square Error (RMSE) and Score metrics. Compared to the state-of-the-art method based on Recurrent Neural Network (RNN) or CNN and its variants, Score is reduced by at least 2.71% and RMSE by at least 3.13%. Compared to the Transformer-based improved method, the Score is decreased by at least 4.54% and the RMSE is decreased by at least 2.78%. The effectiveness of the proposed method is demonstrated.

MHT: A multiscale hourglass-transformer for remaining useful life prediction of aircraft engine

Remaining useful life (RUL) prediction of aircraft engines is significant in the health monitoring, operation, and maintenance of aircraft. Capturing more comprehensive device degradation trends at different time scales and extracting long-term dependencies effectively among elements in long time series are two challenges in the field of aircraft engine RUL estimation. To address the aforementioned challenges, this paper proposes a novel multiscale Hourglass-Transformer (MHT) aircraft engine RUL prognostics. Specifically, an hourglass-shaped multiscale feature extractor (HME) is designed based on one-dimensional convolutional neural network, which can scale the time sequence into multi-time scales for feature fusion. Then, a transformer network is employed to further extract features from the fused feature map and output the RUL. To enhance inter-scale data attention, a pyramid self-attention mechanism is employed in both the encoder and decoder. Finally, the superiority and effectiveness of this approach are verified on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset. Furthermore, the robustness and generalization capability of this method are further validated on New Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS) dataset.

Comparison of Residual-based Methods on Fault Detection

An important initial step in fault detection for complex industrial systems is gaining an understanding of their health condition. Subsequently, continuous monitoring of this health condition becomes crucial to observe its evolution, track changes over time, and isolate faults. As faults are typically rare occurrences, it is essential to perform this monitoring in an unsupervised manner. Various approaches have been proposed not only to detect faults in an unsupervised manner but also to distinguish between different potential fault types. In this study, we perform a comprehensive comparison between two residual-based approaches: autoencoders, and theinput-output models that establish a mapping between operating conditions and sensor readings. We explore the sensorwise residuals and aggregated residuals for the entire system in both methods. The performance evaluation focuses on three tasks: health indicator construction, fault detection, and health indicator interpretation. To perform the comparison, we utilize the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dynamical model, specifically a subset of the turbofan engine dataset containing three different fault types. All models are trained exclusively on healthy data. Fault detection is achieved by applying a threshold that is determined based on the healthy condition. The detection results reveal that both models are capable of detecting faults with an average delay of around 20 cycles and maintain a low false positive rate. While the fault detection performance is similar for both models, the input-output model provides better interpretability regarding potential fault types and the possible faulty components.

An attention-based temporal convolutional network method for predicting remaining useful life of aero-engine

Researches on Remaining Useful Life (RUL) prediction of aero-engine could help to make maintenance plans, improve operation reliabilities and reduce maintenance costs. While deep learning methods have been widely used in RUL prediction research, most deep learning-based RUL prediction methods tend to treat input features as equally important. Contributions of different channels and time steps from input features are not considered simultaneously, which will inevitably affect efficiencies and accuracies of RUL prediction. Therefore, a novel deep learning-based RUL prediction method named attention-based temporal convolutional network (ATCN) is proposed in this article. First, an improved self-attention mechanism is used to weight contributions of different time steps from input features. Input features of time steps closely related to RUL are enhanced by the improved self-attention mechanism, which could improve efficiencies of feature extraction in a network. Then, a temporal convolutional network is constructed to capture long-term dependent information and extract feature representations from weighted features of the improved self-attention mechanism. Next, a squeeze-and-excitation mechanism is adopted to weight contributions of different channels from feature representations, which could help to improve prediction accuracies of the network. Finally, a fully connected layer is constructed to fuse weighted features to output RUL values. A commercial modular aero-propulsion system simulation (C-MAPSS) dataset from NASA is applied to verify effects of the proposed method. Performances of the proposed method are compared with those based on different neural network architectures, such as CNN, RNN, LSTM, DCNN, TCN, BiGRU-TSAM, AGCNN and channel attention plus Transformer. Results show that the proposed method could yield results with higher accuracy for RUL prediction of aero-engine than other methods.

Remaining useful life with self-attention assisted physics-informed neural network

Remaining useful life (RUL) prediction as the key technique of prognostics and health management (PHM) has been extensively investigated. The application of data-driven methods in RUL prediction has advanced greatly in recent years. However, a large number of model parameters, low prediction accuracy, and lack of interpretability of prediction results are common problems of current data-driven methods. In this paper, we propose a Physics-Informed Neural Networks (PINNs) with Self-Attention mechanism-based hybrid framework for aircraft engine RUL prognostics. Specifically, the self-attention mechanism is employed to learn the differences and interactions between features, and reasonably map high-dimensional features to low-dimensional spaces. Subsequently, PINN is utilized to regularize the end-to-end prediction network, which maps features to RUL. The RUL prediction framework termed AttnPINN has verified its superiority on the Commercial Modular AeroPropulsion System Simulation (C-MAPSS) dataset. It achieves state-of-the-art prediction performance with a small number of parameters, resulting in computation-light features. Furthermore, its prediction results are highly interpretable and can accurately predict failure modes, thereby enabling precise predictive maintenance.

Multiscale global and local self-attention-based network for remaining useful life prediction

Remaining useful life (RUL) prediction plays an important role in prognostics and health management (PHM) and can significantly enhance equipment reliability and safety in various engineering applications. Accurate RUL prediction enables proactive maintenance planning, helping prevent potential hazards and economic losses caused by equipment failures. Recently, while deep learning-based methods have swept the RUL prediction field, most existing methods still have difficulties in simultaneously extracting multiscale global and local degradation feature information from raw multi-sensor monitoring data. To address these issues, we propose a novel multiscale global and local self-attention-based network (MGLSN) for RUL prediction. MGLSN consists of global and local feature extraction subnetworks based on self-attention, which work in parallel to simultaneously extract the global and local degradation features of equipment and can adaptively focus on more important parts. While the global network captures long-term dependencies between time steps, the local network focuses on modeling local temporal dynamics. The design of parallel feature extraction can avoid the mutual influence of information from global and local aspects. Moreover, MGLSN adopts a multiscale feature extraction design (multiscale self-attention and convolution) to capture the global and local degradation patterns at different scales, which can be combined to better reflect the degradation trend. Experiments on the widely used Commercial Modular Aero-Propulsion System Simulation (CMAPSS), New CMAPSS (N-CMAPSS), and International Conference on Prognostics and Health Management 2008 challenge datasets provided by NASA show that MGLSN significantly outperforms state-of-the-art RUL prediction methods and has great application prospects in the field of PHM.

MCTAN: A Novel Multichannel Temporal Attention-Based Network for Industrial Health Indicator Prediction.

Health indicator prediction, such as remaining useful life prediction and product quality prediction, is an important aspect of industrial intelligence. It is essential to process the massive multichannel industrial time series collected from the Industrial Internet of Things for the industrial health indicator prediction. At present, there are still three issues that need to be considered for industrial health indicator prediction. First, it is difficult to directly connect the distant positions in the industrial time series to extract the temporal relations, which decreases the efficiency of extracting the potential long-distance temporal relations and training networks. Second, it should be fully considered that data from different channels have different contributions. Equally dealing with the contributions of each channel will weaken the representational ability of prediction networks. Third, the loss function deals with early predictions and delay predictions equally, which will lead to high risks caused by delay predictions. In this article, for these issues, a novel multichannel temporal attention-based network (MCTAN) is proposed for industrial health indicator prediction, which can weigh contributions of different channels through the channel attention while avoiding the loss of the temporal information and directly connect each time series position to the local fields of the sequence through the multi-head local attention mechanism to efficiently extract potential long-distance temporal relations. Then, a weighted mean square error loss function differently dealing with early predictions and delay predictions by setting dynamic weights is presented to reduce delay predictions. Next, to deal with the above-mentioned issues systematically, a framework combining data preprocessing and MCTAN collaboratively is introduced to predict industrial health indicators through multichannel time series. Finally, the experiments are carried out on the commercial modular aero-propulsion system simulation dataset to measure the performances, including the accuracy of industrial health indicator predictions and the inference speed.

Advancing aircraft engine RUL predictions: an interpretable integrated approach of feature engineering and aggregated feature importance

In this study, we present a comprehensive approach for predicting the remaining useful life (RUL) of aircraft engines, incorporating advanced feature engineering, dimensionality reduction, feature selection techniques, and machine learning models. The process begins with a rolling time series window, followed by the extraction of a multitude of statistical features, and the application of principal component analysis for dimensionality reduction. We utilize a variety of feature selection methods, such as Genetic Algorithm, Recursive Feature Elimination, Least Absolute Shrinkage and Selection Operator Regression, and Feature Importances from a Random Forest model. As a significant contribution, we introduce the novel aggregated feature importances with cross-validation (AFICv) technique, which ranks features based on their mean importance. We establish a selection criterion that retains features with a cumulative mean sum equal to 70%, thereby reducing the complexity of machine learning models and enhancing their generalizability. Four machine learning regression models—Natural and Extreme Gradient Boosting, Random Forest, and Multi-Layer Perceptron—were employed to evaluate the effectiveness of the selected features. The performance of our proposed method is assessed by the evaluation metrics Root Mean Square Error (RMSE) and R2 Score, and also considered within-interval percentages and relative accuracy metrics. Importantly, a novel PCA interpretability was introduced to provide real-world context and enhance the utility of our findings for domain experts. Our results indicate that the proposed AFICv technique efficiently achieves competitive performance across the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) sub-datasets using a significantly smaller subset of features, thus contributing to a more effective and interpretable RUL prediction methodology for aircraft engines.

A new multi-sensor fusion with hybrid Convolutional Neural Network with Wiener model for remaining useful life estimation

With the development of smart manufacturing, the health monitoring of the machines has become important. Remaining useful life (RUL) estimation, which could predict the future machine state, has attracted much more attentions. Deep learning (DL) based RUL has achieved remarkable results. But it still faces the issues on the multi-sensor fusion process and the health index (HI) construction, and both of these two issues can affect DL models for RUL. To overcome these issues, this research designed a new hybrid model of Convolutional Neural Network (CNN) and Wiener process, named hybrid CNN-Wiener model. First, the CNN network is adopted to achieve feature-level fusion of multi-sensor signals and to calculate the virtual HI of the machine. Second, the Wiener process model is developed to estimate the value of RUL using virtual HI. Third, the Wiener process model is designed as the layer in CNN network and trained with CNN together. The hybrid CNN-Wiener model has been tested on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset, and its results show that the hybrid CNN-Wiener model has obtained the remarkable promotion by comparing with other famous DL models. The ablation studies have been tested and it shows that the hybrid CNN-Wiener model has been promotion largely with the Wiener model and the multi-sensor fusion techniques.

Fault Prognosis of Turbofan Engines

In the era of industrial big data, prognostics and health management is essential to improve the prediction of future failures to minimize inventory, maintenance, and human costs. Used for the 2021 PHM Data Challenge, the new Commercial Modular Aero-Propulsion System Simulation dataset from NASA is an open-source benchmark containing simulated turbofan engine units flown under realistic flight conditions. Deep learning approaches implemented previously for this application attempt to predict the remaining useful life of the engine units, but have not utilized labeled failure mode information, impeding practical usage and explainability. To address these limitations, a new prognostics approach is formulated with a customized loss function to simultaneously predict the current health state, the eventual failing component(s), and the remaining useful life. The proposed method incorporates principal component analysis to orthogonalize statistical time-domain features, which are inputs into supervised regressors such as random forests, extreme random forests, XGBoost, and artificial neural networks. The highest performing algorithm, ANN–Flux with PCA augmentation, achieves AUROC and AUPR scores exceeding 0.94 for each classification on average. In addition to predicting eventual failures with high accuracy, ANN–Flux achieves comparable remaining useful life RMSE for the same test split of the dataset when benchmarked against past work, with significantly less computational cost.

Adaptively Lightweight Spatiotemporal Information-Extraction-Operator-Based DL Method for Aero-Engine RUL Prediction.

Accurate prediction of machine RUL plays a crucial role in reducing human casualties and economic losses, which is of significance. The ability to handle spatiotemporal information contributes to improving the prediction performance of machine RUL. However, most existing models for spatiotemporal information processing are not only complex in structure but also lack adaptive feature extraction capabilities. Therefore, a lightweight operator with adaptive spatiotemporal information extraction ability named Involution GRU (Inv-GRU) is proposed for aero-engine RUL prediction. Involution, the adaptive feature extraction operator, is replaced by the information connection in the gated recurrent unit to achieve adaptively spatiotemporal information extraction and reduce the parameters. Thus, Inv-GRU can well extract the degradation information of the aero-engine. Then, for the RUL prediction task, the Inv-GRU-based deep learning (DL) framework is firstly constructed, where features extracted by Inv-GRU and several human-made features are separately processed to generate health indicators (HIs) from multi-raw data of aero-engines. Finally, fully connected layers are adopted to reduce the dimension and regress RUL based on the generated HIs. By applying the Inv-GRU-based DL framework to the Commercial Modular Aero Propulsion System Simulation (C-MAPSS) datasets, successful predictions of aero-engines RUL have been achieved. Quantitative comparative experiments have demonstrated the advantage of the proposed method over other approaches in terms of both RUL prediction accuracy and computational burden.

Deep attention SMOTE: Data augmentation with a learnable interpolation factor for imbalanced anomaly detection of gas turbines

Anomaly detection of gas turbines faces the significant challenges of data imbalance and inter-class overlap. In this paper, we develop a novel data augmentation method, namely deep attention synthetic minority over-sampling technique with the Encoder-Decoder (DA-SMOTE-ED), which serves as a key step in our hybrid re-sampling scheme. To reduce the risk of generating noise data, on one hand, the DA-SMOTE-ED leverages an Encoder-Decoder to learn a class-separable feature space to weaken the effect of inter-class overlap. On the other hand, an attention module is applied to assign proper interpolation factors to generate synthetic samples that stay off the aggregation area of normal samples. Moreover, synthetic samples are generated in the learnable feature space, mapped back to the original space, and merged with under-sampled samples to form the balanced dataset. Finally, the superiority of the developed method is validated through two case studies including the real monitoring data of gas turbines and the modified version of the commercial modular aero-propulsion system simulation (C-MAPPS) dataset. More specifically, its average balanced accuracy is 91.77 % on the gas turbine dataset, yielding 3.67 %, 6.4 %, and 5.56 % improvements compared to the SMOTE-ENN, TimeGAN, and AugmentTS, respectively.

Attention and Long Short-Term Memory Network for Remaining Useful Lifetime Predictions of Turbofan Engine Degradation

Machine Prognostics and Health Management (PHM) is often concerned with the prediction of the Remaining Useful Lifetime (RUL) of assets. Accurate real-time RUL predictions enable equipment health assessment and maintenance planning. In this work, we propose a Long Short-Term Memory (LSTM) network combined with global Attention mechanisms to learn RUL relationships directly from time-series sensor data. We use the NASA Commercial Modular Aero- Propulsion System Simulation (C-MAPPS) datasets to assess the performance of our proposed method. We compare our approach with current state-of-the-art methods on the same datasets and show that our results yield competitive results. Moreover, our method does not require previous degradation knowledge, and attention weights can be used to visualise temporal relationships between inputs and predicted outputs.

Time Series-Based Sensor Selection and Lightweight Neural Architecture Search for RUL Estimation in Future Industry 4.0

Industry 4.0 is the current development trend in manufacturing technology. Regarding prognostic and health management (PHM) systems, a major task is to predict the remaining useful life (RUL) of a machine. To have precise RUL information, massive sensors should be involved, which leads to the dramatic cost of sensor network construction. Therefore, many sensor selection methods have been proposed to remove the redundant sensors under a certain constraint of RUL estimation. However, those approaches do not consider time-series sensing data, which is an intrinsic feature of mechanical signals. Therefore, the current research suffers from sensor under-killing problems due to the pessimistic consideration. To solve this problem, this work first considers the time-series sensing data to propose an integrated group-based valuable sensor selection algorithm by using the Least Absolute Shrinkage and Selection Operator (LASSO) property. In addition, to reduce the computing and hardware overhead, we further propose a heuristic neural architecture search (NAS) method to reduce the number of neurons in each neural network for further RUL estimation. To verify the proposed approaches, we use the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset and utilize the PHM score to evaluate the performance of RUL estimation. Compared with the conventional methods, the proposed sensor selection method can reduce the PHM score by 9% to 99% with fewer sensors. On the other hand, the proposed NAS method can reduce the number of neurons by 86% to 89% and reduce the PHM score by 17% to 79% compared with the traditional NAS approaches.

Modified DEMATEL Method Based on Objective Data Grey Relational Analysis for Time Series

Smart data selection can quickly sieve valuable information from initial data. Doing so improves the efficiency of analyzing situations to aid in better decision-making. Past methods have mostly been based on expert experience, which may be subjective and inefficient when dealing with large, complex datasets. Recently, the system analysis method has been exploited to find the key data. However, few studies address the indirect effects and heterogeneity of time series data. In this study, a data selection method, the modified Decision-Making Trial and Evaluation Laboratory (DEMATEL) method based on the objective data grey relational analysis (GRA), is used to enhance the ability to analyze time-series data. GRA was first applied to assess the direct impact in the raw data indicators. Then, a modified DEMATEL was adopted to find the overall impact by including the indirect impact and data heterogeneity. We applied the method to analyze the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset and perform the remaining useful life (RUL) prediction of aircraft engines. The results suggest that our method predicts well. Our work offers a nuanced approach of identifying key information in time series data and has potential applications.

Controlled physics-informed data generation for deep learning-based remaining useful life prediction under unseen operation conditions

Limited availability of representative time-to-failure (TTF) trajectories either limits the performance of deep learning (DL)-based approaches on remaining useful life (RUL) prediction in practice or even precludes their application. Generating synthetic data that is physically plausible is a promising way to tackle this challenge. In this study, a novel hybrid framework combining the controlled physics-informed data generation approach with a deep learning-based prediction model for prognostics is proposed. In the proposed framework, a new controlled physics-informed generative adversarial network (CPI-GAN) is developed to generate synthetic degradation trajectories that are physically interpretable and diverse. Five basic physics constraints are proposed as the controllable settings in the generator. A physics-informed loss function with penalty is designed as the regularization term, which ensures that the changing trend of system health state recorded in the synthetic data is consistent with the underlying physical laws. Then, the generated synthetic data is used as input of the DL-based prediction model to obtain the RUL estimations. The proposed framework is evaluated based on new Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS), a turbofan engine prognostics dataset where a limited availability of TTF trajectories is assumed. The experimental results demonstrate that the proposed framework is able to generate synthetic TTF trajectories that are consistent with underlying degradation trends. The generated trajectories enable to significantly improve the accuracy of RUL predictions.

Pseudo-Label-Vector-Guided Parallel Attention Network for Remaining Useful Life Prediction

Prognostic health management (PHM) has become important in many industries as a critical technology to increase machine stability and operational efficiency. Recently, various methods using deep learning to estimate the remaining useful life (RUL) as a core task of PHM have been proposed. However, the existing attention methods do not explicitly capture the correlation between temporal and spatial time series, reducing the RUL prediction accuracy. This article proposes a novel RUL prediction algorithm using a spatiotemporal attention mechanism based on the pseudo-label vectors to solve this problem. The proposed attention network uses the pseudo-label vector learned in the intermediate prediction process as a query vector to focus on time sequence data related to the RUL. Therefore, compared with conventional attention models that extract correlations for all the sequences, the proposed model captures features directly related to RUL with less computational cost. Experiments have been performed on two widely used datasets, and the experimental results show that the proposed approach outperforms the state of the art for root-mean-square error, with averages 4.27 and 3039 in the NASA Commercial Modular Aero-Propulsion System Simulation dataset and the IEEE PHM 2012 Prognostic challenge dataset, respectively. In addition, the analysis in the experiment reveals that the proposed model has better interpretability than the existing models by obtaining the correlation between time-series data and the RUL through the attention score in terms of time and features.

A new supervised multi-head self-attention autoencoder for health indicator construction and similarity-based machinery RUL prediction

Remaining useful life (RUL) prediction plays a significant role in the prognostic and health management (PHM) of rotating machineries. A good health indicator (HI) can ensure the accuracy and reliability of RUL prediction. However, numerous existing deep learning-based HI construction approaches rely heavily on the prior knowledge, and they are difficult to capture the key information in the process of machinery degradation from raw signals, thereby affecting the performance of RUL prediction. To tackle the aforementioned problem, a new supervised multi-head self-attention autoencoder (SMSAE) is proposed for extracting the HI that effectively reflects the degraded state of rotating machinery. By embedding the multi-head self-attention (MS) module into autoencoder and imposing the constraint of power function-type labels on the hidden variable, SMSAE can directly extract the HIs from raw vibration signals. As the current HI evaluation indexes don’t consider the global monotonicity and variation law of HI, two improved monotonicity and robustness indexes are designed for the better evaluation of HI. With the proposed HI, a two-stage residual life prediction framework based on similarity is developed. Extensive experiments have been performed on an actual wind turbine gearbox bearing dataset and a well-known open commercial modular aero-propulsion system simulation (C-MAPSS) dataset. The comparative results verify that the constructed SMSAE HI has better comprehensive performance than the typical HIs, and the proposed prediction method is competitive with the state-of-the-art methods.