An information-induced fault diagnosis framework generalizing from stationary to unknown nonstationary working conditions (2023)

Rolling bearings are major and crucial components of rotating machinery, and bearing faults may lead to the unplanned shutdown of equipment, which cause economic losses and personnel injuries inevitably. Therefore, accurate fault diagnosis of bearings is necessary for equipment maintenance and it has attracted considerable attention [1], [2], [3].

In recent years, deep learning-based fault diagnosis (DLFD) approaches have achieved notable performance with less human labor and high accuracy [4]. However, the effectiveness of DLFD methods depends on the assumption of independently identically distribution, which requires a consistent distribution of training and test data. In practice, variable operating conditions cause significant changes in the distribution of the vibration signal, thus there are inevitable distribution differences between training data and test data, resulting in performance degradation [5].

To overcome the distribution shift challenge, domain adaptation-based fault diagnosis (DAFD) approaches have been devised, which aim to mitigate the distribution shift between training data (source data) and test data (target data) [6], [7], [8], [9]. Although they break through the limitation of DLFD methods, DAFD methods still face obstacles due to the prerequisite that unlabeled or few labeled target data should be accessible in training process, which is difficult to meet in actual fault diagnosis scenarios since the working conditions of target data are always novel and the target fault data are difficult to be collected in advance [10].

In order to diagnosis faults under novel working conditions without relying on target data, domain generalization-based fault diagnosis (DGFD) methods are emerging, which can build the diagnosis model with one or several different but related source data and then generalize to unseen target data [11]. Despite the achievement of target data-independent, the DGFD methods above focus on diagnostic tasks under different stationary or segmented stationary working conditions, which are too ideal to be applied since bearings in industry generally suffer from strongly non-stationary working conditions with noise pollution [12]. For instance, when high-speed rails accelerate or decelerate, the working condition of bearings is nonstationary, which causes the amplitude of bearings vibration data to fluctuate continuously and irregularly in a certain range as shown in Fig.1, and the fault characteristic frequency may be smeared in the spectrum and continuous blurred spectrum lines appearing on some frequency bands [13]. Compared with segmented stationary working conditions, the non-stationarity working conditions will cause the significant distribution shift and inevitably increase the difficulty of invariant feature learning and generalization. Since a large number of bearing fault data have been collected under stationary conditions from the laboratory, it is practical and economical to generalize diagnosis model from stationary working conditions to unseen non-stationary working conditions.

There are two main reasons why the existing DGFD methods cannot solve the task above. First, as shown in Fig.2(a), the existing DGFD methods attempt to learn both discriminative and domain-invariant features by minimizing the defined classification error and the distribution shift loss. Nevertheless, the distribution shift is quantified using the latent vectors (the unobservable variables output from feature extractors) obtained by minimizing the defined classification error, which does not explicitly infer features from the invariant fault information. As a result, some unnecessary features (i.e. domain-invariant but not fault-caused) may be capture together, such as external vibration disturbances and noise, leading to obvious degradation of diagnosis models when the target domain is significantly different from source domains. Second, as the absence of the target data, the choice of source data encodes the assumption about which target data might be encountered, thus the feature learning is constrained by the diversity of source domains (training data with different distributions). As a result, if the diversity and number of source domains are insufficient, the model will overfitting to source domains and hard to generalize to unknown target domains. For example, if the source data are all collected from constant speeds, “the acceleration responses have periodic impact components with relatively stable amplitudes” may be capture as the invariable feature related to bearing outer race fault, but it is obviously not valid under non-stationary speeds. To expand available dataset, some DGFD methods adopt data manipulation techniques, such as data scaling, noise addition, mixup, and other operations [14], [15], [16]. However, shifts in amplitude and frequency of the vibration signals under nonstationary conditions may be too extreme to be simulated, besides, the useful information related to faults may be corrupted if manipulating the input data directly. Therefore, how to efficiently use the limited data to improve the generalization ability of the model is also a challenge to be solved.

To generalize the fault diagnosis model from stationary working conditions to unseen nonstationary working conditions, As shown in Fig.2(b), this paper propose a novel domain generalization framework named Information Induced Feature Decomposition and Augmentation (IIFDA), which contains an Information Induced Feature Learning Network (IIFLN) and an Augmented Feature Synthesis (AFS) method with feature augmentation techniques extrapolation (EP) and gradient confusion (GC). Instead of extracting latent vectors z by minimizing classification error, the IIFLN uses probability encoder E as the feature extractor to infer reasonable latent distributions with prior information encoded by approximating the prior distributions produced by probability encoder F, where “latent distributions” means given the input x the probability encoder E produces an unobservable distribution p(z|x) (e.g. a Gaussian) over the possible values of z. The principle of IIFLN is shown to be equivalent to maximize the variational lower bound on the marginal likelihood of information. Therefore, the fault-related distribution only contains fault-related features, and other spurious correlation (i.e. domain-invariant but not fault-caused) are ruled out. For better generalization, the AFS is proposed to assist the model in further refining the fault-related features by increasing the diversity of training feature. Unlike previous data augmentation methods manipulating the inputs, the AFS considers the correlation between feature representations and fault patterns, and performs EP and GC in specific feature space not essential for identifying categories but correlated with some fault-unrelated factors (i.e., operational conditions, environment noise in this paper). In this way, diverse features can be synthesized without corrupting fault information. The main contributions of this paper are as follows:

• (1)

  A domain generalization framework IIFDA is proposed to generalize fault diagnosis knowledge from stationary working conditions to unseen nonstationary working conditions, which is important but rarely studied.

• (2)

  A feature learning network IIFLN is proposed to infer the reasonable latent distribution with information encoded, which essentially maximizes the variational lower bound on the marginal likelihood of information to improve the correctness and generalization of feature.

• (3)

  A feature augmentation method AFS with EP and GC is proposed to synthesize diverse features without corrupting fault information, which assists the model in refining fault-related features and allows for better generalization. Due to the independence of the domain number and feature form, it can be extended to other networks.

• (4)

  Comprehensive experiments and ablation studies are conducted on bearing datasets to verify the superiority and effectiveness of IIFDA. The results indicate that IIFDA achieves better performance than state-of-the-art methods in generalizing from constant speeds to unknown nonstationary speeds or unknown sharp variation speeds.

The rest is organized as follows. Section2 introduces the related works, Section3 provides the background concepts, Section4 introduces the detailed information of IIFDA, Section5 presents the experiments and Section6 is the conclusion.