Search Results (13)

Under complex operating conditions, vibration signals from rotating machinery often exhibit non-stationary characteristics with non-proportional and closely spaced instantaneous frequency (IF) components. Traditional time–frequency analysis (TFA) methods struggle to accurately extract such features due to energy leakage and component mixing. In response to these issues, an enhanced time–frequency analysis approach, termed Local Entropy Selection Scaling–Reassigning Chirplet Transform (LESSRCT), has been developed to improve the representation accuracy for complex non-stationary signals. This approach constructs multi-channel time–frequency representations (TFRs) by introducing multiple scales of chirp rates (CRs) and utilizes a Rényi entropy-based criterion to adaptively select multiple optimal CRs at the same time center, enabling accurate characterization of multiple fundamental components. In addition, a frequency reassignment mechanism is incorporated to enhance energy concentration and suppress spectral diffusion. Extensive validation was conducted on a representative synthetic signal and three categories of real-world data—bat echolocation, inner race bearing faults, and wind turbine gearbox vibrations. In each case, the proposed LESSRCT method was compared against SBCT, GLCT, CWT, SET, EMCT, and STFT. On the synthetic signal, LESSRCT achieved the lowest Rényi entropy of 13.53, which was 19.5% lower than that of SET (16.87) and 35% lower than GLCT (18.36). In the bat signal analysis, LESSRCT reached an entropy of 11.53, substantially outperforming CWT (19.91) and SBCT (15.64). For bearing fault diagnosis signals, LESSRCT consistently achieved lower entropy across varying SNR levels compared to all baseline methods, demonstrating strong noise resilience and robustness. The final case on wind turbine signals demonstrated its robustness and computational efficiency, with a runtime of 1.31 s and excellent resolution. These results confirm that LESSRCT delivers robust, high-resolution TFRs with strong noise resilience and broad applicability. It holds strong potential for precise fault detection and condition monitoring in domains such as aerospace and renewable energy systems. Full article

This study addresses the long-standing difficulty of predicting the remaining useful life (RUL) of rolling bearings from highly non-stationary vibration signals by proposing WaveAtten, a symmetry-aware deep learning framework. First, mirror-symmetric and bi-orthogonal Daubechies wavelet filters are applied to decompose each raw signal into multi-scale approximation/detail pairs, explicitly preserving the left–right symmetry that characterizes periodic mechanical responses while isolating asymmetric transient faults. Next, a bidirectional sparse-attention module reinforces this structural symmetry by selecting query–key pairs in a forward/backward balanced fashion, allowing the network to weight homologous spectral patterns and suppress non-symmetric noise. Finally, the symmetry-enhanced features—augmented with temperature and other auxiliary sensor data—are fed into a long short-term memory (LSTM) network that models the symmetric progression of degradation over time. Experiments on the IEEE PHM2012 bearing dataset showed that WaveAtten achieved superior mean squared error, mean absolute error, and R² scores compared with both classical signal-processing pipelines and state-of-the-art deep models, while ablation revealed a 6–8% performance drop when the symmetry-oriented components were removed. By systematically exploiting the intrinsic symmetry of vibration phenomena, WaveAtten offers a robust and efficient route to RUL prediction, paving the way for intelligent, condition-based maintenance of industrial machinery. Full article

This paper investigates the design and performance of a tunable pendulum energy harvester (TPEH) integrated with cone continuously variable transmission (CVT) to enhance energy harvesting efficiency in broadband and non-stationary vibrational environments. The cone CVT mechanism enables the tunability of the harvester’s natural frequency, allowing it to dynamically adapt and maintain resonance across varying excitation frequencies. A specific focus is placed on the system’s behavior under chirp signal base excitation, which simulates a time-varying frequency environment. Experimental and analytical approaches are employed to evaluate the system’s dynamic response, energy output, and frequency adaptation capabilities. The results demonstrate that the proposed TPEH system achieves significant energy harvesting performance improvements by leveraging the cone CVT to optimize power generation under resonance conditions. The system is also shown to be effective in maintaining stable operation over a wide range of frequencies, demonstrating its versatility for real-world vibrational energy harvesting applications. This research highlights the importance of tunability in energy harvesting systems and the role of mechanical transmission mechanisms in improving adaptability. The proposed design has strong potential for applications in environments with non-stationary vibrations, such as transportation systems, industrial machinery, and infrastructure monitoring. Full article

Commonly used methods for identifying modal parameters under environmental excitations assume that the unknown environmental input is a stationary white noise sequence. For large-scale civil structures, actual environmental excitations, such as wind gusts and impact loads, cannot usually meet this condition, and exhibit obvious non-stationary and non-white-noise characteristics. The theoretical basis of the stochastic subspace method is the state-space equation in the time domain, while the state-space equation of the system is only applicable to linear systems. Therefore, under non-smooth excitation, this paper proposes a stochastic subspace method based on RDT. Firstly, this paper uses the random decrement technique of non-stationary excitation to obtain the free attenuation response of the response signal, and then uses the stochastic subspace identification (SSI) method to identify the modal parameters. This not only improves the signal-to-noise ratio of the signal, but also improves the computational efficiency significantly. A non-stationary excitation is applied to the spatial grid structure model, and the RDT-SSI method is used to identify the modal parameters. The identification results show that the proposed method can solve the problem of identifying structural modal parameters under non-stationary excitation. This method is applied to the actual health monitoring of stadium grids, and can also obtain better identification results in frequency, damping ratio, and vibration mode, while also significantly improving computational efficiency. Full article

Rotational speed measuring is important in order tracking under non-stational working conditions. However, sometimes, encoders or coded discs are not easy to mount due to the limited measurement environment. In this paper, a new in situ gravity acceleration decomposition method (GAD) is proposed for rotational speed estimation, and it is applied in the order tracking scene for fault diagnosis of a gearbox under non-stationary working conditions. In the proposed method, a MEMS accelerometer is locally embedded on the rotating shaft or disc in the tangential direction. The time-varying gravity acceleration component is sensed by the in situ accelerometer during the rotation of the shaft or disc. The GAD method is established to exploit the gravity acceleration component based on the linear-phase finite impulse response (FIR) filter and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) methods. Then, the phase signal of time-varying gravity acceleration is derived for rotational speed estimations. A motor–shaft–disc experimental setup is established to verify the correctness and effectiveness of the proposed method in comparison to a mounted encoder. The results show that both the estimated average and instantaneous rotational speed agree well with the mounted encoder. Furthermore, both the proposed GAD method and the traditional vibration-based tacholess speed estimation methods are applied in the context of order tracking for fault diagnosis of a gearbox. The results demonstrate the superiority of the proposed method in the detection of tooth spalling faults under non-stationary working conditions. Full article

Real-time representation of the current performance of structures is an important task for perceiving potential danger in in-service bridges. Methods driven by the multisource sensing data of structural health monitoring systems are an effective way to achieve this goal. Due to the explicit zero-point of signals, the live load-induced response has an inherent advantage for quantitatively representing the performance of bridges. Taking a long-span cable-stayed railway–highway combined bridge as the case study, this paper presents a representation method of in-service performance. First, the non-stationary sections of train-induced response are automatically extracted by wavelet transform and window with threshold. Then, the data of the feature parameter of each non-stationary section are automatically divided into four cases of train load according to the calculational theory of bridge vibration under train effect and clustering analysis. Finally, the performance indexes for structural deformation and dynamics are determined separately, based on hierarchical clustering and statistical modeling. Fusing the real variability of massive data from monitoring and the knowledge of mechanics of theoretical calculations, accurate and robust indexes of bridge deflection distribution and forced vibration frequency are obtained in real time. The whole process verifies the feasibility of the representation of bridge in-service performance from massive multisource sensing data. The presented method, framework, and analysis results can be used as a reference for the design, operation, and maintenance works of long-span railway bridges. Full article

Diagnosing the condition of rotating machines by non-invasive methods is based on the analysis of dynamic signals from sensors mounted on the machine—such as vibration, velocity, or acceleration sensors; torque meters; force sensors; pressure sensors; etc. The article presents a new method combining the empirical mode decomposition algorithm with wavelet leader multifractal formalism applied to diagnosing damages of rotating machines in non-stationary conditions. The development of damage causes an increase in the level of multifractality of the signal. The multifractal spectrum obtained as a result of the algorithm changes its shape. Diagnosis is based on the classification of the features of this spectrum. The method is effective in relation to faults causing impulse responses in the dynamic signal registered by the sensors. The method has been illustrated with examples of vibration signals of rotating machines recorded on a laboratory stand, as well as on real objects. Full article

Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals. Full article

Modal parameters can reflect the dynamic characteristics of the structure and can be used to control vibration. To identify the operational modal parameters of linear slow-time-varying structures only from non-stationary vibration response signals, a method based on moving window locality preserving projections (MWLPP) algorithm is proposed. Based on the theory of “time freeze”, the method selects a fixed length window and takes the displacement response signal in each window as a stationary random sequence. The locality preserving projections algorithm is used to identify the transient modal frequency and modal shape of the structure at this window. The low-dimensional embedding of the displacement response data set calculated by locality preserving projections (LPP) corresponds to the modal coordinate response matrix, and the transformation matrix corresponds to the modal shape matrix. The simulation results of the mass slow-time-varying three degree of freedom (DOF) and the density slow-time-varying cantilever beam show that the new method can effectively identify the modal shape and modal natural frequency of the linear slow-time-varying only from the non-stationary vibration response signal, and the performance is better than the moving window principal component analysis (MWPCA). Full article

From the viewpoint of vibration control, if the amplitude of the main frequencies of the vibration response can be reduced, the vibration energy of the structure is greatly reduced. Modal parameters, including modal shapes, natural frequencies, and damping ratios, can reflect the dynamics of the structure and can be used to control the vibration. This paper integrates the idea of “forgetting factor weighting” into eigenvector recursive principal component analysis, and then proposes an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor (ERPCAWF). The proposed method can identify the transient natural frequencies and transient modal shapes online and realtime using only nonstationary vibration response signals. The identified modal parameters are also suitable for online, real-time health monitoring and fault diagnosis. Finally, the modal identification results from a three-degree-of-freedom weakly damped linear time-varying structure shows that the ERPCAWF-based OMA method can effectively identify transient modal parameters online using only nonstationary response signals. The results also show that the ERPCAWF-based approach is faster, requires less memory space, and achieves higher identification accuracy and greater stability than autocorrelation matrix recursive PCA with a forgetting factor-based OMA. Full article

The fault response signals of an axle-box bearing of a rail vehicle have strongly non-linear and non-stationary characteristics, which can reflect the operating state of the running gears. This paper proposes a novel method for bearing fault diagnosis based on frequency-domain energy feature reconstruction (EFR) and composite multiscale permutation entropy (CMPE). First, a wavelet packet transform (WPT) is applied to decompose the vibration signals into multiple frequency bands. Then, considering that the bearing-localized defects cause the axle-box bearing system to resonate at a high frequency, which will lead to uneven energy distribution of the signal in the frequency domain, the energy factors of each frequency band are calculated by an energy feature extraction algorithm, from which the frequency band with maximum energy factor (which contains abundant fault information) is reconstructed to the time-domain signal. Next, the complexity of the reconstructed signals is calculated by CMPE as fault feature vectors. Finally, the feature vectors are input into a medium Gaussian support vector machine (MG-SVM) for bearing condition classification. The proposed method is validated by a public bearing data set and a wheelset-bearing system test bench data set. The experimental results indicate that the proposed method can effectively extract bearing fault features and provides a new solution for condition monitoring and fault diagnosis of rail vehicle axle-box bearings. Full article

Real-time dynamic displacement and acceleration responses of the main span section of the Tianjin Fumin Bridge in China under ambient excitation were tested using a Global Navigation Satellite System (GNSS) dynamic deformation monitoring system and an acceleration sensor vibration test system. Considering the close relationship between the GNSS multipath errors and measurement environment in combination with the noise reduction characteristics of different filtering algorithms, the researchers proposed an AFEC mixed filtering algorithm, which is an combination of autocorrelation function-based empirical mode decomposition (EMD) and Chebyshev mixed filtering to extract the real vibration displacement of the bridge structure after system error correction and filtering de-noising of signals collected by the GNSS. The proposed AFEC mixed filtering algorithm had high accuracy (1 mm) of real displacement at the elevation direction. Next, the traditional random decrement technique (used mainly for stationary random processes) was expanded to non-stationary random processes. Combining the expanded random decrement technique (RDT) and autoregressive moving average model (ARMA), the modal frequency of the bridge structural system was extracted using an expanded ARMA_RDT modal identification method, which was compared with the power spectrum analysis results of the acceleration signal and finite element analysis results. Identification results demonstrated that the proposed algorithm is applicable to analyze the dynamic displacement monitoring data of real bridge structures under ambient excitation and could identify the first five orders of the inherent frequencies of the structural system accurately. The identification error of the inherent frequency was smaller than 6%, indicating the high identification accuracy of the proposed algorithm. Furthermore, the GNSS dynamic deformation monitoring method can be used to monitor dynamic displacement and identify the modal parameters of bridge structures. The GNSS can monitor the working state of bridges effectively and accurately. Research results can provide references to evaluate the bearing capacity, safety performance, and durability of bridge structures during operation. Full article

The stability of a fiber optic gyroscope (FOG) in measurement while drilling (MWD) could vary with time because of changing temperature, high vibration, and sudden power failure. The dynamic Allan variance (DAVAR) is a sliding version of the Allan variance. It is a practical tool that could represent the non-stationary behavior of the gyroscope signal. Since the normal DAVAR takes too long to deal with long time series, a fast DAVAR algorithm has been developed to accelerate the computation speed. However, both the normal DAVAR algorithm and the fast algorithm become invalid for discontinuous time series. What is worse, the FOG-based MWD underground often keeps working for several days; the gyro data collected aboveground is not only very time-consuming, but also sometimes discontinuous in the timeline. In this article, on the basis of the fast algorithm for DAVAR, we make a further advance in the fast algorithm (improved fast DAVAR) to extend the fast DAVAR to discontinuous time series. The improved fast DAVAR and the normal DAVAR are used to responsively characterize two sets of simulation data. The simulation results show that when the length of the time series is short, the improved fast DAVAR saves 78.93% of calculation time. When the length of the time series is long ( $6\times {10}^5$ samples), the improved fast DAVAR reduces calculation time by 97.09%. Another set of simulation data with missing data is characterized by the improved fast DAVAR. Its simulation results prove that the improved fast DAVAR could successfully deal with discontinuous data. In the end, a vibration experiment with FOGs-based MWD has been implemented to validate the good performance of the improved fast DAVAR. The results of the experience testify that the improved fast DAVAR not only shortens computation time, but could also analyze discontinuous time series. Full article