Diagnosis of compound faults is meaningful and challenging in actual industrial applications. Generally, it is impractical to obtain a sufficient amount of labeled data for the compound faults, which limits the performance of existing methods. The characteristics of compound faults should be fully considered. Hence, reasonably introducing prior knowledge of fault information is of great significance to improve the practicability of diagnostic methods. In this paper, several unsupervised representation extraction techniques are firstly exploited to extract the fault information in the latent space, which is beneficial to alleviate the negative effects of noise disturbance in real-life scenarios. A discrimination-guided active learning method based on marginal representations, termed DGMR, is then proposed. In this case, samples with compound fault information are more likely to be iteratively queried for expert annotation. Several experiments are conducted using realistic experimental platform data. The experimental results show that the proposed DGMR can achieve high diagnostic accuracy for industrial compound fault diagnosis with a small number of annotated samples and shallow classifiers.Note to Practitioners—Compound faults widely exist in complex industrial equipment due to device coupling, which tends to be more diverse and generally exhibits more complex characteristics. In addition, even if the device passes the consistency test, the distribution of data collected by the test device before and after long-term use may have certain deviations due to performance degradation and other factors. Moreover, expert annotation is necessary but cost-sensitive. With the proposed scheme in this paper, vibration signals can be used to construct a fault database through several feature extraction techniques. Compound and unknown fault samples are more likely to be selected. Engineers can provide labels for these small number of fault samples based on methods such as frequency domain analysis, which can reduce the cost of annotations. High diagnostic accuracy can be obtained only using shallow classifiers in this case. Several experiments of a real rotating machinery fault diagnosis test rig are carried out. Experimental results demonstrate that the proposed method outperforms some advanced methods.

In order to ensure the safe and reliable operation of the energy system, real-time fault diagnosis technology is indispensable. Energy systems are typically complex systems consisting of multiple subsystems that are coupled with each other. Before and after the occurrence of a fault, the system is generally in an abnormal or even harsh environment, which may cause a large number of randomly missing measurement data and make the application of fault diagnosis technology extremely difficult. In this paper, the graph attention network (GAT) is improved by a Gaussian mixture model (GMM) for incomplete-data representation. The iteratively updated expectation of the GMM serves as the characterization of missing data, which significantly improves the ability to fill in missing data. The GAT fuses multi-source data according to the topology structure so as to comprehensively exploit the spatial information. The gated recurrent units (GRU) extract dynamic fault information from embedded spatial features and classify the time series into various fault types. Moreover, we propose a loss function in the form of weighted focal loss so that the fault-class imbalance issue brought by the data deficiency can be solved. The proposed uniform spatial-temporal graph neural network classification framework together with the GMM (GM-STGNN) can effectively improve fault diagnosis performance and is applied on an experimental platform of an authentic industrial estate. Results of comparative experiments under different conditions of both sufficient and deficient data illustrate the efficiency and advancement of the proposed method.Note to Practitioners—This paper presents a fault diagnosis method for large-scale energy systems with massive missing data. The proposed GM-STGNN framework can be applied in complex energy networks consisting of coupling subsystems, such as power grids, heating networks, and gas networks. With an incomplete-data representation mechanism, the proposed method utilizes topology information to comprehensively exploit spatial features, it also recurrently transmits historical embedded features and extracts dynamic fault characteristics. Therefore, it can effectively improve energy-network fault identification accuracy when more than half of the sample exists vacant values randomly. In the training procedure, after pre-setting the model scale, data acquired by multi-source sensors is put into the model according to the real topology structure, and corresponding fault labels serve as the supervision. The statistical characteristics of missing data are learned with neural-network parameters until the loss converges. In practical application, the sampling data is divided by a time window of a few seconds. The missing data is mitigated by the estimated expectation of the GMM. Therefore, real-time fault classification results can be obtained with high accuracy. The effectiveness of the proposed method is illustrated by fault diagnosis of a typical distributed heating network under the noise influence. Benefiting from the ability to learn fault knowledge, the proposed method can be easily applied to new scenarios where the process data and topology structure of the system are known.

In the operation process of the rotating machinery, compound faults have various combination forms and are difficult to reproduce, which results in the scarcity of training samples of various compound faults. In this article, a method of partial-label learning and classification fusion is proposed to investigate the above problems. Wavelet packet transformation and dimensionless parameterization are utilized to extract features in high-dimensional space. A label-specific feature learning architecture is proposed to make up for the shortage of handcrafted features. An improved focal loss is exploited for learning prominent compound-fault characteristics and imbalanced fault samples. Basic probability assignments about fault classes are generated from each partial classifier and combined to obtain a final inference about fault types. Experimental results of single-fault and compound-fault classification illustrate the effectiveness of the proposed method.

The feature of multienergy flows of the integrated energy system (IES) causes the relationship among different types of subsystems to be complex. In order to handle the compound-fault diagnosis problem of the IES with small sample sizes of compound faults, in this article, a novel multiscale spatial-temporal graph neural network (MSSTGN) is proposed for fault detection and compound-fault identification. The label-specific fault features are learned by multiscale graph operators and gated recurrent units in the spatial and temporal domains, respectively. The deficiency of limited compound fault samples is mitigated by fusing partial inferences by base MSSTGN classifiers trained for paired faults. Constant data features of each fault class are enhanced by the proposed loss functions with a center loss. The advantages of the proposed method are illustrated by comparative experiments exploiting the process data from an IES under multiple situations of missing data and noise influence.

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.

We propose a general framework of using a multi-level log-Gaussian Cox process to model repeatedly observed point processes with complex structures; such type of data has become increasingly available in various areas including medical research, social sciences, economics, and finance due to technological advances. A novel nonparametric approach is developed to efficiently and consistently estimate the covariance functions of the latent Gaussian processes at all levels. To predict the functional principal component scores, we propose a consistent estimation procedure by maximizing the conditional likelihood of super-positions of point processes. We further extend our procedure to the bivariate point process case in which potential correlations between the processes can be assessed. Asymptotic properties of the proposed estimators are investigated, and the effectiveness of our procedures is illustrated through a simulation study and an application to a stock trading dataset.