Blades are the core components of rotating machinery, and the blade vibration status directly impacts the working efficiency and safe operation of the equipment. The blade tip timing (BTT) technique provides a solution for blade vibration monitoring and is currently a prominent topic in research on blade vibration issues. Nevertheless, the non-stationary factors present in actual engineering applications introduce inaccuracies in the BTT technique, resulting in blade vibration measurement errors. The theory of blade vibration difference offers a new perspective for high-precision BTT techniques. This paper optimizes the traditional circumferential Fourier fitting (CFF) algorithm. According to the blade departure time measurement mechanism, four sets of BTT signals are obtained by two probes, six sets of blade vibration differences are established, and, then, a blade vibration difference-based circumferential Fourier fitting (BVD-CFF) algorithm for blade synchronous vibration parameter identification is proposed. Simulation studies demonstrate that the BVD-CFF algorithm exhibits superior anti-noise performance. Moreover, experimental investigations on a high-speed rotation blade vibration test rig and a large-scale centrifugal compressor test rig display that the engine order of blade synchronous vibrations obtained by the BVD-CFF algorithm are essentially the same as those obtained by the strain gauge method.

Rotating machinery is widely used in modern industrial systems, and its health status can directly impact the operation of the entire system. Timely and accurate diagnosis of rotating machinery faults is crucial for ensuring production safety, reducing economic losses, and improving efficiency. Traditional deep learning methods can only extract features from the vertices of the input data, thereby overlooking the information contained in the relationships between vertices. This paper proposes a Legendre graph convolutional network (LGCN) integrated with a self-attention graph pooling method, which is applied to fault diagnosis of rotating machinery. The SA-LGCN model converts vibration signals from Euclidean space into graph signals in non-Euclidean space, employing a fast local spectral filter based on Legendre polynomials and a self-attention graph pooling method, significantly improving the model’s stability and computational efficiency. By applying the proposed method to 10 different planetary gearbox fault tasks, we verify that it offers significant advantages in fault diagnosis accuracy and load adaptability under various working conditions.

Recent research in cross-domain intelligence fault diagnosis of machinery still has some problems, such as relatively ideal speed conditions and sample conditions. In engineering practice, the rotational speed of the machine is often transient and time-varying, which makes the sample annotation increasingly expensive. Meanwhile, the number of samples collected from different health states is often unbalanced. To deal with the above challenges, a complementary-label (CL) adversarial domain adaptation fault diagnosis network (CLADAN) is proposed under time-varying rotational speed and weakly-supervised conditions. In the weakly supervised learning condition, machine prior information is used for sample annotation via cost-friendly complementary label learning. A diagnostic model learning strategy with discretized category probabilities is designed to avoid multi-peak distribution of prediction results. In adversarial training process, we developed virtual adversarial regularization (VAR) strategy, which further enhances the robustness of the model by adding adversarial perturbations in the target domain. Comparative experiments on two case studies validated the superior performance of the proposed method.

In practical engineering, the asymmetric problem of the domain label space is inevitable owing to the prior fault information of the target domain being difficult to completely obtain. This implies that the target domain may include unseen fault classes or lack certain fault classes found in the source domain. To maintain diagnostic performance and knowledge generalization across different speeds, cross-domain intelligent fault diagnosis (IFD) models are widely researched. However, the rigid requirement for consistent domain label spaces hinders the IFD model from identifying private fault patterns in the target domain. In practical engineering, the asymmetric domain label space problem is inevitable, as the target domain’s fault prior information is difficult to completely obtain. This means that the target domain may have unseen fault classes or lack some source domain fault classes. To address these challenges, we propose an asymmetric cross-domain IFD method with label position matching and boundary sparse learning (ASY-WLB). It reduces the IFD model’s dependence on domain label space symmetry during transient speed variation. To integrate signal prior knowledge for transferable feature representation, angular resampling is used to lessen the time-varying speed fluctuations’ impact on the IFD model. We design a label-positioning information compensation mechanism and weighted contrastive domain discrepancy, accurately matching unseen class label information and constraining the diagnosis model’s decision boundary from a data conditional distribution perspective. Finally, extensive experiments on two time-varying speed datasets demonstrate our method’s superiority.

Blade tip timing (BTT) is a core technique for investigating the blade vibration of large-scale centrifugal compressors, and identifying the parameters of blade asynchronous vibration is crucial for implementing blade condition monitoring based on the BTT technique. In this study, the multiple signal classification (MUSIC) algorithm and the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm were first applied separately to identify the asynchronous vibration parameters of centrifugal compressor blades, with their advantages and disadvantages discussed. Subsequently, based on the frequency distribution characteristics in the ESPRIT results, the concept of “frequency distribution rate” was proposed. Finally, the results of the MUSIC algorithm were weighted by the frequency distribution rate, and an improved MUSIC algorithm was proposed. This enhanced confidence in the real frequency in the MUSIC algorithm results. Compared with the strain gauge method, the maximum relative error of the improved algorithm is 0.23%. The improved MUSIC algorithm improves the accuracy of parameter identification for blade asynchronous vibration, which holds great significance for the industrial application of the BTT technique.

As a powerful tool for sparse signal representation, dictionary learning has gained traction in data-driven fault diagnosis. However, noise interference exists in actual industrial environments; noise as a common feature across all classes inevitably covers discriminative features, thereby impairing the diagnostic performance of methods reliant on dictionary learning. To tackle this challenge, this paper proposes a multi-sensor dictionary fusion-driven sparse representation classification method. The initial step involves leveraging a low-rank shared dictionary learning technique to extract discriminative dictionaries from multi-sensor data. A dictionary fusion metric is introduced based on dictionary reconstructability, dictionary discriminativity, and sparse code discriminability to fuse dictionaries from different sensors. Second, a sparse code discriminative enhancement method is proposed, which suppresses sparse code in non-correct projection regions by setting them to zero, thereby reducing the contribution of sparse code from incorrect projection areas. A classification framework grounded in sparse representation is then formulated. Validation experiments on two distinct planetary gearbox datasets (a laboratory planetary gearbox dataset and the southeast university planetary gearbox dataset) reveal that the multi-sensor dictionary fusion-driven sparse representation classification method attains 99.95% and 99.94% classification accuracy. Comparative analyses further substantiate its exceptional diagnostic precision against contemporary advanced techniques.