Due to the heavy background noise and strong interference, a blurry or even false time-frequency (TF) representation (TFR) by synchrosqueezing wavelet transform (SST) always results in inaccurate or meaningless gear fault extractions. To solve this problem, a novel TF analysis (TFA) method termed dual-core denoised SST is proposed in this article. The concepts critical to the proposed method are: 1) The dual-core denoising is proposed. First, the measured signal is transformed to the binary tree structure of the prewhitening and pseudo-characterizing signals by cepstrum editing. Second, two empirical mode decomposition (EMD)-based denoising techniques are, respectively, proposed for each binary-tree signal, focused on extracting different gear features such as the modulation and transients. Then, the purified feature signal is obtained by mixing the dual-core denoising results. 2) The multistep denoising strategy is studied for further improving the denoising accuracy. The steps are determined by the Rényi entropy. 3) By the multistep dual-core denoising, the denoised TFR with such meaningful TF signatures of gear faults as the accurate demodulation components and distinct transients could be obtained for gear fault detection. The repeatable simulations and engineering applications are used to verify the performance of denoising and TF resolution enhancement for gear fault detection.

The meaningful data-based fault diagnosis is beforehand revealing the potential faults to reduce the costly breakdowns, one challenging of which is extracting the weak features from the complicated signals. Ensemble noise-reconstructed EMD (ENEMD) is an intelligent method by the nice integration of adaptively decomposing and naturally denoising. However, ENEMD still suffers from such issues as the false possible noise-only IMFs and the universal minimax threshold, reducing the precision of the critical noise estimation for the weak feature extraction. Thus, the dual-mode noise-reconstructed EMD method is proposed for weak feature extraction and fault diagnosis of rotating machinery. First, the possible noise-only IMF selection rule is redesigned according to the noise characteristic and the correlation evaluation, to eliminate the redundant slowly oscillating IMFs mistakenly chosen for noise estimation. Second, the adaptive local minimax threshold is proposed in the noise estimation technique for the low SNR signal, to overcome the drawback of additionally keeping some critical but weak fault features into the estimation noise. Hereinto, the local threshold is respectively performed in each sliding window defined by the demodulated rotating-related feature frequency. Third, the proposed method is addressed with the flowchart. Finally, two engineering case studies are implemented to demonstrate the feasibility and effectiveness of the method. The analytic results show that the method could effectively extract the periodic impulses generating by the early local damage in the gearbox of a hot strip finishing mill. Meanwhile, the method could successfully reveal the weak rubbing-impact faults along with alleviating the mode mixing phenomenon in the refined results for fault diagnosis of a heavy oil catalytic cracking unit. Hence, the method could provide a promising tool for weak feature extraction and fault diagnosis of rotating machinery.

The gear fault signal is characterized by strong and/or weak impulsive features and is often accompanied by strong background noise, which makes the gear fault feature extraction more difficult. Hence, this paper proposes a new time-frequency analysis method called the tensor denoising (TD) assisted time-reassigned synchrosqueezing wavelet transform (TD-TSWT). First, to improve the accuracy of subsequent time-frequency analysis, a TD method based on high-order singular value decomposition is proposed as a preprocessing technique according to the cyclostationary characteristics of gear faults and the Hankel matrix. Meanwhile, combined with the advantages of sample entropy calculation, the concept of using sample entropy to determine the reasonable singular order is proposed. Second, to propose TSWT for revealing gear fault features. TSWT by introducing continuous wavelet transform to obtain the basis function which is more similar to gear fault impulses. Moreover, according to the properties of the gear fault signal, the group delay estimation operator in the frequency domain is designed for TSWT, which is more suitable for the gear fault feature extraction. Finally, the results of simulations and engineering cases show that the method provides a useful tool for the diagnosis of gear faults.

Fault diagnosis with formal languages can be performed in an interpretable way. However, the traditional formal languages cannot deal with noisy environments. Additionally, finding the optimal formal language for fault diagnosis is still a challenge due to the sparse reward issue. This article presents a novel method to find formal languages, written with signal spectral logic (SSL), to describe the fault behaviors among frequency domain for fault diagnosis. The formal language defined by SSL is robust to noise, acts as the fault diagnoser, and provides interpretabilities for human operators. Moreover, the fault diagnoser construction procedure has been formulated as a language generation process and an adversarial training technique is used to find the optimal formal language and avoid sparse reward issue existing in language generation problems. Some experiments with real rolling element bearing data and simulated signals demonstrate that our method is able to find formal languages to diagnose faults efficiently and accurately under noisy environments.

Multichannel signals contain an abundance of fault characteristic information on equipment and show greater potential for weak fault characteristics extraction and early fault detection. However, how to effectively utilize the advantages of multichannel signals with their information richness while eliminating interference components caused by strong background noise and information redundancy to achieve accurate extraction of fault characteristics is still challenging for mechanical fault diagnosis based on multichannel signals. To address this issue, an effective weak fault detection framework for multichannel signals is proposed in this paper. Firstly, the advantages of a tensor on characterizing fault information were displayed, and the low-rank property of multichannel fault signals in a tensor domain is revealed through tensor singular value decomposition. Secondly, to tackle weak fault characteristics extraction from multichannel signals under strong background noise, an adaptive threshold function is introduced, and an adaptive low-rank tensor estimation model is constructed. Thirdly, to further improve the accurate estimation of weak fault characteristics from multichannel signals, a new sparsity metric-oriented parameter optimization strategy is provided for the adaptive low-rank tensor estimation model. Finally, an effective multichannel weak fault detection framework is formed for rolling bearings. Multichannel data from the repeatable simulation, the publicly available XJTU-SY whole lifetime datasets and an accelerated fatigue test of rolling bearings are used to validate the effectiveness and practicality of the proposed method. Excellent results are obtained in multichannel weak fault detection with strong background noise, especially for early fault detection.

Performance degradation assessment (PDA) is of great significance to ensure safety and availability of mechanical equipment. As an important issue of PDA, the robustness of the trained model directly affects the assessment efficiency and restricts its application in practice. This paper proposes a robust modeling approach based on Student’s t-hidden Markov model (Student’s t-HMM) and nuisance attribute projection (NAP). NAP can remove nuisance attributes caused by individual differences from the feature space. Student’s t-HMM utilizes the finite Student’s t-mixture models (SMMs) to describe the observation emission densities associated with each hidden state, which can be more tolerant towards outliers than conventional HMMs. Based on these two techniques, the proposed method is supposed to be more robust and can assess the performance degradation process of new objects based on data of tested objects. The superiority of the proposed approach is evaluated using the vibration data from the accelerated life tests of bearings and the public XJTU-SY Bearing Datasets. The results demonstrate the robustness and effectiveness of the proposed approach for PDA modeling of rolling element bearings.