Deflection influence line identification under moving vehicle based on variational modal decomposition and B-spline basis function

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

The vehicle scanning method (VSM) is widely used for bridge damage identification (BDI) because it relies solely on vehicle dynamic responses. The recently introduced contact point response, which is derived from vehicle dynamics but devoid of vehicle-related natural frequencies, shows great potential for application in the vehicle scanning method. However, its application in bridge damage detection remains understudied. The aim of this paper is to propose a new bridge damage identification method based on the contact point response. The method uses variational modal decomposition (VMD) to solve the problem of mode mixing and spurious frequencies in the signal. The continuous wavelet transform (CWT) is then utilized for damage identification. The introduction of variational modal decomposition makes the extracted signal more accurate, thus enabling more accurate damage identification. Numerical simulations validate the method’s robustness under varying conditions, including the vehicle speed, wavelet scale factors, the number of bridge spans, and pavement roughness. The results demonstrate that variational modal decomposition eliminates signal artifacts, producing smooth variational modal decomposition–continuous wavelet transform curves for accurate damage detection. In this study, we offer a robust and practical solution for bridge health monitoring using the vehicle scanning method.

Rotating machinery contains numerous rolling bearings, which are critical for ensuring the normal working position and accurate operation of individual shaft systems. However, damage to rolling bearings can change their damping, stiffness, and elastic force. As a result, fault signals appear nonlinear and nonstationary. Vibration signals thus become difficult to diagnose clearly, especially in the incipient fault stage. To solve this problem, this article proposes an intelligent approach based on variational mode decomposition and the self-organizing feature map for rolling bearing fault diagnosis. First, the intrinsic mode function components of rolling bearing vibration signals are effectively separated by variational mode decomposition. Then, permutation entropy is used to extract feature vectors, which are used as training and testing data for the self-organizing feature map network. Finally, the various fault types of states are clustered on an intuitive visualization map. Clustering results of the experimental signal and the measured signal prove that the proposed method can successfully extract and cluster the rolling bearing faults in engineering applications. The proposed method improves the fault recognition rate to some extent over traditional methods.

When identifying damage to an offshore wind turbine (OWT) support structure, the influence of harmonic components in vibration response and the difficulty of acquiring data in the damaged state will be encountered. Therefore, the current paper employs the variational mode decomposition (VMD) and sim‐to‐real deep transfer learning (TL) to identify the damage to an OWT support structure. To eliminate the effect of harmonic components, the vibration response is decomposed using VMD, and the modal response’s reconstructed signal (only containing the structure’s natural frequency) is selected for damage identification. The numerical simulation data and the model test’s measured data are utilized as the source domain (SD) and target domain (TD), respectively. The source model is established by training a convolutional neural network (CNN) with the SD data. The source model’s network structure and weight are frozen to the TD network’s corresponding position. The measured data are utilized to fine‐tune the parameters to establish a target model, which is tested to attain the damage identification outcomes. The presented method is validated using the model test data of an OWT support structure.

Purpose Aiming at the problems of high cost, high risk and traffic impact of in situ load testing of Bridges after fire, this paper proposes a fire bridge structural damage identification method based on a fire dynamics simulator (FDS)-Kriging model modification and a unit modal strain energy damage index, so as to effectively assess the damage of bridge structures after fire. Determine whether it can continue to be used and whether it affects driving safety. Design/methodology/approach Propose a fire bridge structural damage identification method to establish the FDS-Kriging model correction. Findings The finite element model of the fire bridge modified using FDS-Kriging approach can reflect the actual situation of the bridge structure more accurately, and the damage location and degree identified by the modal strain energy method are consistent with the actual bridge. Therefore, the effectiveness of the proposed method has been verified, and a new strategy for fire bridge damage identification has been provided. Research demonstrates that the finite element model of the fire-damaged bridge, modified using the FDS-Kriging method, can more accurately reflect the actual structural state. Moreover, the damage location and severity identified via the modal strain energy method align well with the actual bridge conditions. Thus, the effectiveness and engineering applicability of the proposed method are validated, offering a comprehensive new strategy and technical support for the integrated performance evaluation, damage identification and reliability analysis of fire-damaged bridges. Originality/value By determining the finite element correction interval and combining it with the Kriging model, the method realizes the fine correction of the finite element model of the fire bridge. Structural damage identification is carried out by using the unit modal strain energy damage index. This verifies the effectiveness and engineering applicability of the proposed method, which offers a novel approach and technical support for the comprehensive performance evaluation, damage identification and reliability analysis of fire-damaged bridges.

This paper presents analysis and classification of a pathological speech called cold speech, which is recorded when the person is suffering from common cold. Nose and throat are affected by the common cold. As nose and throat play an important role in speech production, the speech characteristics are altered during this pathology. In this work, variational mode decomposition (VMD) is used for analysis and classification of cold speech. VMD decomposes the speech signal into a number of sub-signals or modes. These sub-signals may better exploit the pathological information for characterization of cold speech. Various statistics, mean, variance, kurtosis and skewness are extracted from each of the decomposed sub-signals. Along with those statistics, center frequency, energy, peak amplitude, spectral entropy, permutation entropy and Renyi's entropy are evaluated, and used as features. Mutual information (MI) is further employed to assign the weight values to the features. In terms of classification rates, the proposed feature outperforms the linear prediction coefficients (LPC), mel frequency cepstral coefficients (MFCC), Teager energy operator (TEO) based feature and ComParE feature sets (IS09-emotion and IS13-ComParE). The proposed feature shows an average recognition rate of 90.02 percent for IITG cold speech database and 66.84 percent for URTIC database.

To address the issue of rolling bearing fault diagnosis, this paper proposes a novel model combining the Improved Gorilla Troop Optimization (IGTO) algorithm, Variational Mode Decomposition (VMD), Permutation Entropy (PE), and Long Short-Term Memory (LSTM) networks. The IGTO algorithm is used to optimize the parameters of VMD and LSTM, enhancing signal decomposition and feature extraction. The proposed model achieves fault classification accuracies of 96.67% and 98.96% in the testing and training phases, respectively, on the Case Western Reserve University dataset, with minimal accuracy fluctuations. Furthermore, on the Jiangnan University dataset, the model reaches an average testing accuracy of 98.85%, with the highest accuracy reaching 99.48%. The results also demonstrate high stability, as indicated by low standard deviations (1.2148 and 1.3217) and narrow 95% confidence intervals ([95.75%, 97.58%] and [96.73%, 97.49%]). Despite a longer average runtime of 13.88 s per sample, the model’s superior accuracy justifies the computational cost. These results demonstrate the model’s excellent diagnostic performance, adaptability to different datasets, and practical applicability for rolling bearing fault diagnosis. This approach provides a valuable reference for predictive maintenance and fault detection systems in industrial applications.

High-G MEMS accelerometer (HGMA) is a new type of sensor; it has been widely used in high precision measurement and control fields. Inevitably, the accelerometer output signal contains random noise caused by the accelerometer itself, the hardware circuit and other aspects. In order to denoise the HGMA’s output signal to improve the measurement accuracy, the improved VMD and TFPF hybrid denoising algorithm is proposed, which combines variational modal decomposition (VMD) and time-frequency peak filtering (TFPF). Firstly, VMD was optimized by the multi-objective particle swarm optimization (MOPSO), then the best decomposition parameters [kbest, abest] could be obtained, in which the permutation entropy (PE) and fuzzy entropy (FE) were selected for MOPSO as fitness functions. Secondly, the accelerometer voltage output signals were decomposed by the improved VMD, then some intrinsic mode functions (IMFs) were achieved. Thirdly, sample entropy (SE) was introduced to classify those IMFs into information-dominated IMFs or noise-dominated IMFs. Then, the short-window TFPF was selected for denoising information-dominated IMFs, while the long-window TFPF was selected for denoising noise-dominated IMFs, which can make denoising more targeted. After reconstruction, we obtained the accelerometer denoising signal. The denoising results of different denoising algorithms in the time and frequency domains were compared, and SNR and RMSE were taken as denoising indicators. The improved VMD and TFPF denoising method has a smaller signal distortion and stronger denoising ability, so it can be adopted to denoise the output signal of the High-G MEMS accelerometer to improve its accuracy.

An accurate prediction of carbon pricing is essential in carbon emission management, and also provides an important role for governments to formulate corresponding policies. However, due to the inherent complexity and dynamics of carbon price sequence, the effectiveness of different decomposition algorithms for carbon price remains to be tested. In addition, existing studies lack a systematic framework to explore the organic integration of external factors and secondary decomposition technology, and the feature processing of complex external factors still needs to be improved. In order to overcome the shortcomings of existing research, This paper presents a Variational Modal Decomposition(VMD) algorithm and a Complete Ensemble Empirical Mode Decomposition with Adaptive Second decomposition technology of Noise(CEEMDAN) decomposition algorithm, and extract the features of external factors by Extreme Gradient Boosting (XGBoost) algorithm. The HI-VMD-PE-CEEMDAN-XGBoost-Transformer model for predicting carbon price is constructed by the combined Transformer algorithm. Specifically, first, we use Hampel identifer(HI) to detect and rectify the anomalies in the original sequence. After applying Variational Mode Decomposition(VMD) decomposition algorithm, Permutation Entropy(PE) is utilized to reassemble the decomposed component. Quadratic Decomposition is performed by Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN) algorithm. Then, the XGBoost algorithm is employed to extract features of external factors and screen key factors as predictive input variables. Finally, Transformer, which has stronger capability of large-scale data parallel processing, is selected as the prediction model to achieve a more scientific and effective carbon price prediction. The empirical analysis results based on EU carbon market data verify the validity and superiority of the proposed model in different forecasting scenarios.

Although the technical requirements for the feature extraction of ship radiated noise (SRN) in the fields of national defense and economy increase with each passing day, the complexity of the marine environment makes the feature extraction of SRN difficult. The traditional feature extraction method based on variational mode decomposition (VMD) is widely used in the feature extraction of SRN. Nevertheless, the use of VMD is greatly affected by parameters. In this paper, the butterfly optimization algorithm (BOA) is introduced to optimize VMD, which is called BOA-VMD algorithm, and realizes the optimal selection of VMD parameters K and α. To further improve the efficiency of feature extraction method, combined with slope entropy (SE), a feature extraction method of SRN based on BOA-VMD and SE is proposed. The experimental results of the simulated signal show that the BOA-VMD algorithm has a smaller envelope entropy value and better decomposition effect than the genetic algorithm (GA) and particle swarm optimization (PSO). The experimental results of feature extraction of SRN show that the highest recognition rate of the four entropy values improve with the increase of the number of extracted features, compared with the three entropy values of dispersion entropy (DE), fluctuation dispersion entropy (FDE) and permutation entropy (PE), the SRN feature extraction method based on BOA-VMD and SE has the highest recognition rate under different quantity features, and the recognition rate has reached 100% under three features.

Aiming at the problem that it is difficult to select the appropriate number of decompositions K and penalty factor α for the denoising of plastic pipe leakage signal by variational modal decomposition (VMD) algorithm. In this paper, a noise reduction method based on Whale optimization algorithm (WOA) combined with VMD algorithm was proposed. First, the permutation entropy can reflect the complexity of the one-dimensional time series, and the decomposition result with the smallest permutation entropy is taken as the optimization objective; then the permutation entropy is used as a fitness function combined with WOA to optimize the parameters of the VMD algorithm to realize the adaptive decomposition of the leakage signal; Finally, calculate the correlation coefficient of each intrinsic mode function (IMF) component after decomposition to judge its noise level, remove the high frequency component which contains much noise, so as to realize the noise reduction of pipeline leakage signal. The simulate experimental results show that the method has a good denoising effect on the leakage signal of plastic pipeline, and can effectively improve the signal-to-noise ratio (SNR) of the leakage signal, which proves its feasibility in the actual leakage detection of plastic pipeline.

Bridge damping ratios are extracted via the skillful use of the single-degree-of-freedom (DOF) test vehicle for the first time in this paper. Central to the simultaneous retrieval of the first few frequencies and damping ratios from the contact (point) response of the bridge is the use of the variational mode decomposition (VMD) and random-decrement technique (RDT). Closed-form solutions are newly derived for the vehicle and contact responses of the damped bridge and validated later numerically. Using the proposed method, one calculates first the mono-component from the contact response by the VMD; then extracts the free-decay response for each mode by the RDT; and finally identifies the frequency and damping ratio by the Hilbert transform. The parametric study confirms that: (1) the contact response outperforms vehicle’s response in retrieving bridge frequencies and damping ratios; (2) the first few frequencies can be identified with robustness for reasonable levels of road roughness, vehicle speed, bridge damping and noise; (1) good result is obtained for the first damping ratio, in spite of the traditional uncertainty existing with damping; and (2) ongoing traffic can enhance the proposed method for bridge identification.

As sensor monitoring technology continues to evolve, structural online monitoring and health management have found numerous applications across various fields. However, challenges remain concerning the real-time diagnosis of structural damage and the accuracy of dynamic reliability predictions. In this paper, a structural online damage identification and dynamic reliability prediction method based on Unscented Kalman Filter (UKF) is presented. Specifically, in the Wiener degradation process with random effects on structural performance, the structural damage identification is initially realized using UKF. Following that, the EM algorithm is employed for estimating the performance model parameters. Eventually, dynamic reliability prediction is realized based on conditional probability. The simulation results indicate that the method effectively estimates the damage state during the structure’s use while providing accurate, real-time, and dynamic reliability predictions for the system.

Cable is an important role in Curtain wall cable structures. In order to detect cable damage in a timely and accurate manner, this paper focuses on the problem of non-stationary nonlinear vibration information and mode mixing in Empirical Mode Decomposition (EMD) itself. Based on the damage detection method combining Variational Mode Decomposition (VMD) and Hilbert Transform (HT), further parameter optimization is carried out. This method determines the penalty factor and decomposition level K by searching for the minimum envelope entropy. VMD is used to decompose the vibration information into different BIMF components, and then Hilbert transform is applied to the extracted components to obtain the corresponding marginal spectrum. cable damage identification is performed based on the modal anomaly index. This article confirms through local damage analysis of a single cable that this method can effectively identify the damage location and degree of the cable.