To solve the intractable problems of optimal rank truncation threshold and dominant modes selection strategy of the standard dynamic mode decomposition (DMD), an improved DMD algorithm is introduced in this paper. Distinct from the conventional methods, a convex optimization framework is introduced by applying a parameterized non-convex penalty function to obtain the optimal rank truncation number. This method is inspirited by the performance that it is more perfectible than other rank truncation methods in inhibiting noise disturbance. A hierarchical and multiresolution application similar to the process of wavelet packet decomposition in modes selection is presented so as to improve the algorithm’s performance. With the modes selection strategy, the frequency spectrum of the reconstruction signal is more readable and interference-free. The improved DMD algorithm successfully extracts the fault characteristics of rolling bearing fault signals when it is utilized for mechanical signal feature extraction. Results demonstrated that the proposed method has good application prospects in denoising and fault feature extraction for mechanical signals.

Fault vibration signals of rolling bearings in early stages are affected by complex transmission paths and strong background noise, resulting in weak information about fault characteristics, which is difficult to extract clearly and accurately. To this end, a new diagnosis method for early faults of rolling bearings is proposed. First, the parameter-adaptive multipoint optimal minimum entropy deconvolution adjusted (PA-MOMEDA) algorithm is used to preprocess the fault signals by strengthening their shock components and weakening the influence of noise on their results. Second, the maximum envelope-spectrum characteristic energy ratio is employed as the selection criterion for the optimal truncation order of dynamic mode decomposition (DMD) to decompose and reconstruct the signals. Finally, the processed signals are subjected to the Hilbert envelope spectral transformation to accurately extract early fault characteristic frequencies. An analysis of simulated signals, public database signals, and bearing signals from a wind turbine has shown that the proposed PA-MOMEDA–DMD method can successfully extract the early fault characteristics of rolling bearings. Compared with the traditional pattern decomposition algorithms, the proposed method is much better at extracting fault characteristics and diagnosing early faults of rolling bearings. The facts have proved that the proposed method is promising in engineering applications.

Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction.

Dynamic mode decomposition (DMD) has certain advantages compared with the traditional fault signal diagnosis method. By exploiting the strength of DMD algorithm in signal processing, this paper proposes a joint fault diagnosis scheme to extract the spatial and temporal patterns and evaluate them for the complexity to diagnose the fault for one‐dimensional mechanical signal. The multiscale method is adopted to decompose the reconstructed matrix of standard DMD modes into multiple scales with a given level parameter. Total least squares DMD algorithm is performed on each level to solve the noise sensitivity problem. Approximate entropy (ApEn) is performed on the grouped multiscale spatiotemporal modes that represent the dynamic characteristic information of the original signal. ApEn values are used as a fault recognizer to identify fault types. By applying the algorithm on three experimental mechanical vibration data, we verify the effectiveness of the proposed method. The result demonstrates that the proposed scheme can effectively recognize different fault forms as a fault diagnosis method.

Metal structures of ladle cranes are typical complex welded structures, where fatigue cracks are prone to initiate in some specific locations. In this paper, on-site tests and theoretical analysis were performed for a in-service ladle crane to investigate the crack damage mechanism at some local areas beneath the wheel loads. The on-site tests included crack observation of the entire bridge structure, geometry inspection of the main girder and stress test of the key locations. It was found that fatigue cracks had densely occurred in some spots with similar geometry details. The stress test results showed that obvious rail gnawing phenomenon happened during the ladle crane operating process. By finite element analysis (FEA) with a multi-layer model and DLOAD subroutine, stress time histories of the damaged spots under moving wheel loads were simulated. Combined with the tested stresses, influences of rail gnawing force on the stress cycling characteristics at the cracked areas were analyzed. Based on the in-service stress spectrum, the fatigue lives of the cracked areas were predicted, revealing that the random rail gnawing force is the dominant factor causing large amount of cracks at the damaged areas.

Remaining useful life prediction of rolling bearings highly relies on feature extraction of signals. The use of denoising algorithms helps to better eliminate noise and extract features, thereby constructing health indicators to predict remaining useful life. This paper proposes a novel adaptive denoising method based on iterative feature mode decomposition (IFMD) to accurately and efficiently extract fault features. The feature mode decomposition (FMD) employs correlation kurtosis (CK) as the objective function for iterative filter bank updates, enabling rapid identification of fault features. To achieve IFMD, the sparrow search algorithm combines sine-cosine algorithm and cauchy variation (SCSSA) to optimize two key parameters in FMD. During the continuous iteration process of the SCSSA algorithm, filter length and number of modes were determined. IFMD does not require empirical setting of initial parameters. During iterative process, the signal is accurately decomposed and the noise is eliminated. Compared with other optimization algorithms, SCSSA has obvious advantages in iterative rate and global optimization. The envelope spectrum feature energy ratio (ES-FER) is used to select decomposed modes, and the mode with the largest ES-FER is chosen as the optimal mode. Bearing fault diagnosis is realized by envelope spectrum analysis of the optimal mode. The numerical simulations and experimental verifications both validate the effectiveness and superiority of the proposed IFMD in mechanical fault diagnosis.