This study presents a two-step fault diagnosis scheme combined with statistical classification and random forests-based classification for rolling element bearings. Considering the inequality of features sensitivity in different diagnosis steps, the proposed method utilizes permutation entropy and variational mode decomposition to depict vibration signals under single scale and multiscale. In the first step, the permutation entropy features on the single scale of original signals are extracted and the statistical classification model based on Chebyshev’s inequality is constructed to detect the faults with a preliminary acquaintance of the bearing condition. In the second step, vibration signals with fault conditions are firstly decomposed into a collection of intrinsic mode functions by using variational mode decomposition and then multiscale permutation entropy features derived from each mono-component are extracted to identify the specific fault types. In order to improve the classification ability of the characteristic data, the out-of-bag estimation of random forests is firstly employed to reelect and refine the original multiscale permutation entropy features. Then the refined features are considered as the input data to train the random forests-based classification model. Finally, the condition data of bearings with different fault conditions are employed to evaluate the performance of the proposed method. The results indicate that the proposed method can effectively identify the working conditions and fault types of rolling element bearings.

Accurate health evolution trend forecasting of aero-engine is essential for operation reliability and maintenance costs of aeronautical equipment. In this study, an intelligent deep learning method, systematically blending the dispersion entropy-based multi-scale series aggregation scheme and long short term memory (LSTM) neural network, is proposed for forecasting the health evolution trend of aero-engine. Firstly, a comprehensive measurement of health levels, namely, integrated health state index (IHSI), is developed with high-dimensional dataset. Secondly, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is exploited to decompose the IHSI sequence into several multi-scale series to further capture the internal characteristics of original sequence. Subsequently, multi-scale series aggregation assisted with dispersion entropy analysis theory is conducted for obtaining the aggregated sub-series (ASS). Finally, the ASS are served as the inputs of LSTM network to complete the health evolution trend forecasting of aero-engine. To demonstrate the effectiveness of the proposed method, six approaches are present for the comparisons of forecasting performance. The experimental results indicate that the proposed method can effectively measure the health evolution process of aero-engine and further obtain more accurate trend forecasting results.

Rolling bearing is of great importance in modern industrial products, the failure of which may result in accidents and economic losses. Therefore, fault diagnosis of rolling bearing is significant and necessary and can enhance the reliability and efficiency of mechanical systems. Therefore, a novel fault diagnosis method for rolling bearing based on semi-supervised clustering and support vector data description (SVDD) with adaptive parameter optimization and improved decision strategy is proposed in this study. First, variational mode decomposition (VMD) was applied to decompose the vibration signals into sets of intrinsic mode functions (IMFs), where the decomposing mode number K was determined by the central frequency observation method. Next, fuzzy entropy (FuzzyEn) values of all IMFs were calculated to construct the feature vectors of different types of faults. Later, training samples were clustered with semi-supervised fuzzy C-means clustering (SSFCM) for fully exploiting the information inside samples, whereupon a small number of labeled samples were able to provide sufficient data distribution information for subsequent SVDD algorithms and improve its recognition ability. Afterwards, SVDD with improved decision strategy (ID-SVDD) that combined with k-nearest neighbor was proposed to establish diagnostic model. Simultaneously, the optimal parameters C and σ for ID-SVDD were searched by the newly proposed sine cosine algorithm improved with adaptive updating strategy (ASCA). Finally, the proposed diagnosis method was applied for engineering application as well as contrastive analysis. The obtained results reveal that the proposed method exhibits the best performance in all evaluation metrics and has advantages over other comparison methods in both precision and stability.

The Takagi–Sugeno (T–S) fuzzy model identification is a very powerful tool for modelling of complicated nonlinear system. However, the traditional T-S fuzzy model typically uses the L2-norm loss function, which is very sensitive to outliers or noises. So an unreliable model may be obtained due to the presence of outliers or noises. In this paper, the outliers and noises robust T-S fuzzy model identification method based on the fuzzy c-regression model (FCRM) clustering and the L1-norm loss function is proposed. The hyper-plane-shaped clustering algorithm has been proved to be more effective than hyper-sphere-shaped clustering algorithm in T-S fuzzy model identification. Therefore the FCRM clustering algorithm is used in T-S fuzzy model identification for structure identification in the antecedent part. A mass of relevant researches have pointed out that the L1-norm loss function is more robust to outliers and noises than L2-norm loss function. In order to reduce the negative influence of outliers and noises, the L1-norm loss function is employed to enhance the robustness of T-S fuzzy model instead of the L2-norm loss function in the consequent part. Regression and classification applications have been used to demonstrate the validity of the proposed method. The experimental results show that the proposed method has significantly improved the modelling accuracy in dealing with data contaminated by outliers and noises compared with other algorithms.

Fault identification under variable operating conditions is a task of great importance and challenge for equipment health management. However, when dealing with this kind of issue, traditional fault diagnosis methods based on the assumption of the distribution coherence of the training and testing set are no longer applicable. In this paper, a novel state identification method integrated by time-frequency decomposition, multi-information entropies, and joint distribution adaptation is proposed for rolling element bearings. At first, fast ensemble empirical mode decomposition was employed to decompose the vibration signals into a collection of intrinsic mode functions, aiming at obtaining the multiscale description of the original signals. Then, hybrid entropy features that can characterize the dynamic and complexity of time series in the local space, global space, and frequency domain were extracted from each intrinsic mode function. As for the training and testing set under different load conditions, all data was mapped into a reproducing space by joint distribution adaptation to reduce the distribution discrepancies between datasets, where the pseudolabels of the testing set and the final diagnostic results were obtained by the k-nearest neighbor algorithm. Finally, five cases with the training and testing set under variable load conditions were used to demonstrate the performance of the proposed method, and comparisons with some other diagnosis models combined with the same features and other dimensionality reduction methods were also discussed. The analysis results show that the proposed method can effectively recognize the multifaults of rolling element bearings under variable load conditions with higher accuracies and has sound practicability.

The application of wind power interval prediction for power systems attempts to give more comprehensive support to dispatchers and operators of the grid. Lower upper bound estimation (LUBE) method is widely applied in interval prediction. However, the existing LUBE approaches are trained by meta-heuristic optimization, which is either time-consuming or show poor effect when the LUBE model is complex. In this paper, a deep interval prediction method is designed in the framework of LUBE and an efficient gradient descend (GD) training approach is proposed to train the LUBE model. In this method, the long short-term memory is selected as a representative to show the modelling approach. The architecture of the proposed model consists of three parts, namely the long short-term memory module, the fully connected layers and the rank ordered module. Two loss functions are specially designed for implementing the GD training method based on the root mean square back propagation algorithm. To verify the performance of the proposed model, conventional LUBE models, as well as popular statistic interval prediction models are compared in numerical experiments. The results show that the proposed approach performs best in terms of effectiveness and efficiency with average 45% promotion in quality of prediction interval and 66% reduction of time consumptions compared to traditional LUBE models.