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.

Section snippets

Related works

Domain-invariant representation learning and data manipulation are two common categories of domain generalization methods [17]. Domain-invariant representation learning focuses on learning the domain-invariant (or domain-shared) representations for better generalization. Data manipulation focuses on increasing the quantity and diversity of the input data to assist in learning general representations, and it is usually combined with domain-invariant representation learning in DGFD methods to

Problem definition

Bearings in industry such as high-speed trains generally suffer from unknown non-stationary working conditions because of variations in operation conditions and environmental noise interference, and the target fault data are inaccessible during model training. A domain generalization framework named IIFDA is proposed to address this challenge task.

During model training of this work, only training data of several different distributions (source domains) can be obtained from constant operating

Proposed method

To generalize a bearing fault diagnosis model from stationary working conditions to unseen non-stationary working conditions, a fault diagnosis framework named Information Induced Feature Decomposition and Augmentation (IIFDA) is proposed in this paper. The overall framework and the optimization details are introduced below.


In this section, comprehensive experiments are implemented to verify the performance of the proposed methods in the intractable diagnosis problems, and it should be noted that only fault data under stationary working conditions can be used to train the model.


This study proposes an IIFDA framework towards generalizing diagnosis knowledge from stationary working conditions to unknown non-stationary working conditions. IIFDA comprises IIFLN structure and AFS method. IIFLN infers the information-related distributions to promote the extracted features generalization, while the AFS method manipulates the feature space on this basis to increases diversity of the trained features. Extensive experiments and ablation studies conducted on two test rigs to

CRediT authorship contribution statement

Jianing Liu: Methodology, Software, Investigation, Writing – original draft. Hongrui Cao: Conceptualization, Formal analysis, Writing – review & editing. Yang Luo: Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


This work was supported by the National Key R&D Program of China (Grant No. 2020YFB2007700).

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What are three types of system faults you may encounter in the diagnostic process? ›

They include intermittent faults, multi-system faults, faults introduced as a result of system repairs, and indirect faults caused by the influence of external systems, requiring the application of complex diagnostic processes to resolve.

What are the various types of information available for fault diagnosis? ›

Fault diagnosis methods are broadly classified into three main categories: model-based, hardware-based and history-based.

What is the process of fault diagnosis? ›

Therefore, intelligent fault diagnosis becomes a hot topic and it includes the following three steps: signal acquisition, feature extraction, and selection based on the signal processing techniques, and fault recognition based on artificial intelligence techniques.

What is fault detection and diagnosis model? ›

Fault detection and diagnosis methods are mainly divided into three categories as quantitative, qualitative, and data- driven. Quantitative models need an accurate process model based on system governing equations such as momentum, energy, and mass conservation equations, chemical kinetics, and thermodynamic equations.

What are the three most common types of faults? ›

Fault Types
  • Normal fault. A dip-slip fault in which the block above the fault has moved downward relative to the block below. ...
  • Reverse fault. A dip-slip fault in which the upper block, above the fault plane, moves up and over the lower block. ...
  • Strike-slip fault. A fault on which the two blocks slide past one another.
Oct 17, 2017

What are 4 types of diagnostic testing? ›

There are many different types of diagnostic procedures. Examples include laboratory tests (such as blood and urine tests), imaging tests (such as mammography and CT scan), endoscopy (such as colonoscopy and bronchoscopy), and biopsy.

What are the four methods of diagnosis? ›

In Chinese medicine, Observation, Auscultation, Interrogation and Palpation are called as four diagnosis methods which are to collect the medical history of patients and also the ways to treat the disease.

How do you evaluate information for fault diagnosis? ›

What are the six key steps to approach electrical fault finding?
  1. Collect the Evidence. All the evidence collected must be relevant to the problem at hand. ...
  2. Analyse the Evidence. ...
  3. Locate the Fault. ...
  4. Determination and Removal of the Cause. ...
  5. Rectification of the Fault. ...
  6. Check the System.
Jun 17, 2022

What is the difference between fault diagnosis and fault detection? ›

Fault detection is based on signal and process mathematical models, while fault diagnosis is focused on systems theory and process modeling. Monitoring and supervision complement each other in fault management, thus enabling normal and continuous operation.

What is the first step when diagnosing a reported fault? ›

The first step in any fault diagnosis process is to identify the problem clearly and precisely. This means defining the symptoms, the expected performance, the scope, and the urgency of the issue.

What are the 4 types of fault model? ›

Fault surfaces are often nearly planar, and that planar surface is referred to as a “fault plane.” There are four types of faulting -- normal, reverse, strike-slip, and oblique.

What are the classification of faults? ›

Types of faults include strike-slip faults, normal faults, reverse faults, thrust faults, and oblique-slip faults. It can be small and large complex interconnection fault systems and can replace one type of fault in one location with another type in another. Many faults are associated with folds.

What are the three causes of faults? ›

There are three causes to faults: tensional stress, compressional stress, and shear stress. Tensional stress happens when rocks are pulled away from each other; compressional stress, on the other hand, happens when rocks are pushed towards each other.

What are the 3 types of faults characteristics? ›

There are three different types of faults: Normal, Reverse, and Transcurrent (Strike-Slip).
  • Normal faults form when the hanging wall drops down. ...
  • Reverse faults form when the hanging wall moves up. ...
  • Transcurrent or Strike-slip faults have walls that move sideways, not up or down.

What are the 7 commonly performed diagnostic tests? ›

What are the 7 common Diagnostic Tests?
  • X-rays. ...
  • CT scan. ...
  • MRI. ...
  • Mammogram. ...
  • Ultrasound. ...
  • PET scans. ...
  • Pathology test:
Jun 23, 2022

What is the most commonly used diagnostic test? ›

Chest x-rays are one of the most commonly performed diagnostic medical tests. This test provides a black-and-white image of your lungs, heart, and chest wall. The test is noninvasive, painless, and takes just a few minutes.

What are the two different examples of diagnostic testing? ›

Diagnostic tests
  • Biopsy. A biopsy helps a doctor diagnose a medical condition. ...
  • Colonoscopy. ...
  • CT scan. ...
  • CT scans and radiation exposure in children and young people. ...
  • Electrocardiogram (ECG) ...
  • Electroencephalogram (EEG) ...
  • Gastroscopy. ...
  • Eye tests.

What are the basic method of diagnosis? ›

The steps of the diagnostic process fall into three broad categories: Initial Diagnostic Assessment – Patient history, physical exam, evaluation of the patient's chief complaint and symptoms, forming a differential diagnosis, and ordering of diagnostic tests.

What are the specific methods of diagnosis? ›

  • Blood tests. A technician obtains a sample of blood by inserting a needle into a vein, usually in the arm.
  • Urine tests. This painless test requires you to urinate into a container. ...
  • Throat swabs. ...
  • Stool sample. ...
  • Spinal tap (lumbar puncture).
Feb 18, 2022

What are the five steps to fault finding? ›

  • Step 1 – Observe. Most faults provide obvious clues as to their cause. ...
  • Step 2 – Define Problem Area. ...
  • Step 3 – Identify Possible Causes. ...
  • Step 4 – Determine Most Probable Cause. ...
  • Step 5 – Test and Repair.

Why is fault detection and diagnosis important? ›

In conclusion, FDD is an important tool for maintaining the reliability and efficiency of various systems. By detecting and diagnosing faults early on, organizations can take steps to address the problem before it leads to costly downtime or equipment damage.

What is the general method of fault finding? ›

Recommended approach to fault finding

Divide the equipment into logical systems. Test each system functions to specification. Test each component in the failed system operates as it ought. Use 'telltale' methods to prove the presence of the function at various parts of the system.

What is the most common fault model? ›

The most widely used fault model for digital logic fault diagnosis is the stuck-at fault model for its simplicity. Using the stuck-at fault model to simulate logic diagnosis, it is essential to get first a set of possible defective gates with stuck-at faults in its inputs or outputs.

What is the fault model? ›

A fault model is an engineering model of something that could go wrong in the construction or operation of a piece of equipment. From the model, the designer or user can then predict the consequences of this particular fault.

What are the most common fault types? ›

Line to ground fault (L-G) is most common fault and 65-70 percent of faults are of this type. It causes the conductor to make contact with earth or ground. 15 to 20 percent of faults are double line to ground and causes the two conductors to make contact with ground.

What is the most common type of fault in 3 phase system? ›

Fault 1: The single-pole-to-ground short circuit

Regardless of the selected network form: The most common error is always the ground fault. The following figure shows a single-pole to ground fault.

What are the three steps of diagnostic process? ›

The patient is likely the first person to consider his or her symptoms and may choose at this point to engage with the health care system. Once a patient seeks health care, there is an iterative process of information gathering, information integration and interpretation, and determining a working diagnosis.

What is fault in 3 phase system? ›

A three-phase fault usually develops first as a phase-earth fault, and it may be unbalanced. Even when a circuit-breaker closes on to a three-phase fault, one phase may momentarily be faulted before the other two, a matter of importance in high speed protection. Figure 35.1 shows the relevant phasor diagram.

What are the four 4 types of faults? ›

Fault surfaces are often nearly planar, and that planar surface is referred to as a “fault plane.” There are four types of faulting -- normal, reverse, strike-slip, and oblique.

What is the most common type of fault occurrence in the system? ›

Line to ground fault (L-G) is most common fault and 65-70 percent of faults are of this type. It causes the conductor to make contact with earth or ground.

What are the 3 major types of faults explain each and provide an example for each type? ›

There are three different types of faults: Normal, Reverse, and Transcurrent (Strike-Slip).
  • Normal faults form when the hanging wall drops down. ...
  • Reverse faults form when the hanging wall moves up. ...
  • Transcurrent or Strike-slip faults have walls that move sideways, not up or down.

What are the 4 major components of diagnostic reasoning? ›

Elshtein explained four components in the diagnostic reasoning process: cue acquisition hypothesis generation, cue interpretation and hypothesis evaluation which all working in a cycle.

What are the fault stages? ›

2, fault diagnosis consists of three stages: detection, isolation, and estimation. Fault detection is to check whether a fault has occurred. Fault isolation is to locate in which system component a fault has occurred.

What causes three phase fault? ›

Or when all three phase wires short to each other by themselves or with ground contact. A transmission crossarm breaks and drops all three phase wires to the ground. All three phase wires make contact with the earth at the same time causing a 3 phase fault.


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