Regarding the importance of bridges as one of the most critical infrastructures, their maintenance, and health monitoring is of high priority. Interaction between the moving vehicles and bridges is amongst the fields of study that have been investigated in depth by numerous researchers in the field of bridge engineering. Among different proposed methods of structural health monitoring of bridges, the indirect methods that do not need the healthy structure response are of high interest because of their ease and low maintenance costs. The response of a moving mass passing through a bridge can be analyzed for the indirect prediction of the beam's mechanical properties. This can lead to the detection of possible damages or degradations in the structure. By mounting high precision accelerometers on the moving vehicle and recording the corresponding signals, it is possible to capture the sudden change of mechanical properties pertaining to the existence of damage in the bridge. In the current study, an FE code is developed in order to analyze the moving vehicle response. In this code, the bridge is modeled as an Euler-Bernoulli beam, and a complete model comprising stiffness and damping of the suspension system of moving vehicle is built. In order to verify the results of the code, comparisons are made with the outcomes of modal analysis. The sensitivity of the FE results with respect to the number of elements is examined. These comparisons clearly show that both methods reach the same values for a sufficiently high number of elements for the moving vehicle response. Following verification of the code, a brief review of the concepts underlying the Variational mode decomposition ((VMD)) method is given for a self-contained representation. The (VMD) can be used to decompose a signal into a number of signals with limited bandwidth. Although it has found many applications in different signal processing cases (e. g. in the field of electronics, mechanical vibrations of machines, or even in the analysis of economic and financial time series), extending its application to the field of structural health monitoring is entirely a recent and ongoing topic of research. After the introduction of the (VMD), damage in the beams is implemented by using fracture mechanics concepts. Different damage scenarios are applied in order to check the reliability and robustness of using (VMD) as a damage detection method. These include different damage locations (single, dual) and damage severity represented in terms of crack depth. By having a reliable means for the analysis, the novel Variational mode decomposition ((VMD)) is applied to analyze the signals recorded from the vehicle's back axel in search of any possible irregularity in the signal properties. By monitoring results attained for several damage cases, the following conclusions can be given: •,The Variational mode decomposition ((VMD)) can highlight the presence of irregularities in mechanical properties that can be reached directly from decomposed signals. •,The location of these signal irregularities coincides with the presumed location(s) of the crack(s). •,The severity of the signal irregularity and corresponding instantaneous energy is proportional to the degree of damage imposed on the beam. •,The moving vehicle's natural frequency plays an essential role in the bridges' structural health monitoring. The signal processing results exhibit amplified abrupt changes for the vehicles with the natural frequencies close to the beam's fundamental frequencies. Regarding the above conclusions, analyzing moving mass response with the (VMD) can be a reliable damage detection technique.

Background: Electrocardiogram (ECG) plays a vital role in the analysis of heart activity. It can be used to analyze the different heart diseases and mental stress assessment also. Various noises, such as baseline wandering, muscle artifacts and power line interface disturbs the information within the ECG signal. To acquire correct information from ECG signal, these noises should be removed. Methods: In the proposed work, the improved Variational mode decomposition (I(VMD)) method for the removal of noise in ECG signals is used. In the proposed method, the weighted signal amplitude integrated over the timeframe of the ECG signal varies the window size during decomposition. Raw ECG data are extracted from 10 subjects and ECG data are also taken from the MIT BIH database for the proposed method. Results: The performance comparison of traditional Variational mode decomposition ((VMD)) and the proposed technique is also calculated using mean square error, percentage root mean square difference, signal to noise ratio and correlation coefficient. The extracted highest signal to noise ratio (SNR) value of acquired ECG signals using traditional (VMD) is 42db whereas highest value of signal to noise ratio (SNR) using improved (VMD) (I(VMD)) is 83db. Conclusion: The proposed I(VMD) technique represented better performance than traditional (VMD) for denoising of ECG signals.

In this study, the Variational mode decomposition ((VMD)) algorithm was used to identify the modal characteristics of the structure using the decomposition of the acceleration responses recorded by the sensors. This algorithm has advantages over other signal decomposition methods that is resistant to the noise and sampling frequency. Also, the (VMD) algorithm extracts the natural frequencies of the structure concurrently. In addition, the damping ratios of the structure were estimated by fitting a linear function to the logarithmic diagram of the modal response in the decaying amplitude and calculating the slope of this line. The efficiency and accuracy of this algorithm were investigated by decomposing the acceleration responses obtained from the sensors installed on a prestressed concrete bridge (PSCB) that is located under the load of passing vehicles. The (VMD) algorithm was used for signal processing in MATLAB to estimate the natural frequencies, damping ratios and mode shapes of the bridge and ARTeMIS was utilized to verify the results. In addition, the finite element modeling and modal analysis of the bridge were performed in ABAQUS and the natural frequencies and mode shapes of the bridge were obtained. The results showed that the mode shapes estimated by the (VMD) algorithm were in good agreement with the finite element model and ARTeMIS. Also, the damping ratios estimated by this algorithm were obtained close to the damping value of the prestressed concrete bridge. The difference between the frequencies calculated by the (VMD) algorithm and ARTeMIS was about 1%, and the difference with the finite element model frequencies was close to 5%.

Seismic imaging is highly dependent on the quality of seismic data. Structural and stratigraphic interpretation of seismic sections that contain the least amount of noise is much easier. Reflection seismic data are often associated with noise. Coherent noise is a major category of noise that accompanies seismic data, and has the same trend in different seismic traces of the data. Ground roll is one of the main coherent noises that has a low frequency, high amplitude and low velocity. Various methods, such as frequency filters and frequency-wavenumber filter, have been used for ground-roll attenuation. Different advantages and disadvantages are mentioned for each of the methods. In this paper, we have used time – frequency transform and Variational mode decomposition to attenuate the ground-roll.

Denoising is an important step in seismic data processing that can improve the results of other processing steps and, consequently, the interpretation of seismic sections. Both land and marine seismic data contain coherent and incoherent noise. Swell noise is one of the noises present in marine seismic data. It has a high amplitude and low frequency band and is observed as vertical bands in marine seismic data. Developing methods that can attenuate swell noise more while causing the least damage to the signal in marine seismic data seems necessary. There are various methods for attenuating swell noise, each with its advantages and limitations. The approach of most denoising methods is to maximize the separation of noise from the signal. Variational mode decomposition ((VMD)) has shown promising results in seismic denoising by separating different modes of signal and noise. The goal is to obtain a set of intrinsic mode functions (IMFs) and their corresponding center frequencies. The main approach of (VMD) is to decompose the input signal into a number of sub-signals (modes), which also have sparsity properties while recovering the input signal. Here, the sparsity of each mode is chosen as the bandwidth of that mode. In other words, it is assumed that each mode is more concentrated around the center frequency, which is determined in the decomposition. Another important issue in noise attenuation is that the denoising method should be able to perform the denoising process automatically with minimal user intervention. The proposed denoising algorithm in this paper consists of four steps: decomposition, identification, filtering, and reconstruction. In the first step, the seismic signal is decomposed into its constituent modes using the (VMD) method. In the second step, the modes contaminated with noise is identified according to the autocorrelation function of the modes, where the higher values of standard deviation of autocorrelation above a predefined measure present noisy modes. In the third step, the noise is removed through a filtering process based on a hard thresholding procedure. In the final step, the constituent modes, including the clean untouched modes, the denoised modes, and the residue, are summed together and the signal is denoised. The proposed algorithm's efficacy is demonstrated through its application to both synthetic and real seismic data. Notably, the method demonstrates superior performance compared to conventional high-pass filtering and time-frquency denoising (TFDN) method, effectively attenuating swell noise while preserving valuable low-frequency seismic information.

Background and purpose: One of the key indicators in discussions about air quality is the concentration of PM2. 5 particulate matter. This research employs a combined model that utilizes the maximum overlap discrete wavelet transform, Variational mode decomposition, and backpropagation neural network (MODWT-(VMD)-BPNN). This two-stage decomposition technique aims to predict PM2. 5 levels in the city of Urmia. Material and Methods: Data on air quality in Urmia City, including levels of particulate matter (PM10 and PM2. 5), carbon dioxide (CO2), sulfur dioxide (SO2), nitrogen dioxide (NO2), and nitrogen monoxide (NO), were obtained from the General Directorate of Environmental Protection for the years 2019 to 2023. Meteorological data were sourced from the General Directorate of Meteorology of West Azerbaijan Province. In the first stage of the analysis, the original PM2. 5 data series was decomposed into two high-frequency detail levels (d1 and d2) and one low-frequency approximation level (a2) using the Maximum Overlap Discrete Wavelet Transform (MODWT) model. In the second stage, each of these detail and approximation levels was further decomposed into eight variable modes using the Variable mode decomposition ((VMD)) model. Subsequently, each variable mode was simulated and predicted using a backpropagation neural network (BPNN). To evaluate the accuracy and performance of the proposed model, it was compared with the MODWT-BPNN, (VMD)-BPNN, and standard BPNN models. Results: After reviewing the results, the MODWT-(VMD)-BPNN model achieved R=0. 92, RMSE=3. 8074, and MAE=2. 8582 during training, and R=0. 80, RMSE=2. 7679, and MAE=2. 1840 during testing, demonstrating superior accuracy and performance compared to the other models. Conclusion: The two-stage decomposition models tackle mode mixing effectively and enhance the extraction and prediction of multiple frequencies in PM2. 5 data with greater precision. Open Access Policy: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit https: //creativecommons. org/licenses/by/4. 0/

Generative models try to obtain a probability distribution that is similar to that of observed data. Two different solutions have been proposed in this regard in recent years: one is to minimize the divergence (distance) between the two distributions by maximizing the Variational lower bound, and the other is to implicitly reduce the distance between the two distributions through adversarial processes. One of the problems in generative adversarial networks (GANs) is the mode collapse. mode collapse is a phenomenon in which, for various inputs, the generative model generates low variety or similar images. This paper tries to provide a solution to the mode collapse problem proposing a novel method called Variational generative adversarial networks (VGANs). This method exploits Variational autoencoders to initialize GANs. In other words, in addition to maximizing the Variational lower bound, it also implicitly reduces the distance between the two distributions. Experimental results show that this method can deal with the mode collapse problem better than the state-of-the-art. Moreover, in the qualitative analysis, according to a survey of 136 people on the authenticity of the generated images, the proposed method can generate images more similar to real ones.

The price of EU Allowances (EUAs) serves as a mechanism for managing greenhouse gas emissions, influenced by various factors such as economic, financial, political, and other indicators. This study assesses the impact of 31 different energy, financial, and commodity indices on EUA prices. To achieve this, a hybrid data-driven approach is employed. Initially, the Autoregressive Integrated Moving Average (ARIMA) algorithm cleans the relevant data. Subsequently, the Variational mode decomposition ((VMD)) method decomposes the indices into intrinsic mode functions (IMFs). These IMFs are categorized into three-time scales: short-term, medium-term, and long-term. Next, by integrating Recursive Feature Elimination (RFE) and Random Forest (RF) with cross-validation, the most influential features across these time scales are selected. The results demonstrate that the model achieves higher accuracy in medium-term and long-term time scales. Forecasting the price fluctuations of EUAs using these hybrid approaches can contribute to more precise and timely decision-making in policy formulation and investment strategies.