Wavelet Decomposition Level Research Articles

Evaluation of wavelet decomposition level to enhance numerical analysis of seismic responses

In this study, the discrete wavelet transform (DWT) is used to enhance the efficiency of numerical analysis by decomposing earthquake excitation signals into low- and high-frequency components. The low-frequency components, considered as the main damaging factor in earthquake waves, stored in approximation coefficients have been used to perform time response analysis. In the selection of the ground motions, the special attention is given to the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV). An ensemble of nine earthquake records have been selected and used. For each earthquake, displacement response spectra have been generated for both the original signal and its approximations at different DWT levels. To determine the most accurate decomposition level, the normalized root-mean-squared error (NRMSE) of wavelet energy has been computed in spectral displacement responses. The outcomes reveal a dependency of the decomposition level on the specific characteristics of each earthquake. Subsequently, structural analyses are conducted on base-isolated structures with varying story numbers, to examine the accuracy of decomposed signals. Employing both the original signal and its approximations to the structures, base mat displacements and roof accelerations are computed. The findings of the seismic analyses demonstrate the effectiveness of the proposed decomposition levels.

Underwater acoustic target recognition based on multi-resolution wavelet feature deep learning

The application of underwater acoustic target recognition is extensive, exploration of marine resources, submarine vehicle detection and so on. However, traditional feature extraction methods are susceptible to the influence of complex marine environments and target operating conditions, leading to a significant reduction in the correct recognition rate. This paper introduces an underwater acoustic target recognition method that integrates multi-resolution wavelet features with deep learning algorithms, aiming to overcome the limitations of traditional time-frequency analysis techniques, which are unable to extract multiple signal characteristics simultaneously due to the trade-off between time and frequency resolution. Specifically, the essence of this technique is twofold: (1) Selecting suitable wavelet bases and decomposition levels to capture signal characteristics at different resolutions, effectively seizing the signal's local features within the time-frequency domain; (2) Fusing signal features across different resolutions to optimize the feature extraction process and enhance the distinguishability of target features. Finally, by applying deep learning algorithms to experimentally measured underwater acoustic data, the results demonstrate that this method can effectively enhance the accuracy of underwater acoustic target recognition.

Quantification of attenuation and speckle features from endoscopic OCT images for the diagnosis of human brain glioma

Application of optical coherence tomography (OCT) in neurosurgery mostly includes the discrimination between intact and malignant tissues aimed at the detection of brain tumor margins. For particular tissue types, the existing approaches demonstrate low performance, which stimulates the further research for their improvement. The analysis of speckle patterns of brain OCT images is proposed to be taken into account for the discrimination between human brain glioma tissue and intact cortex and white matter. The speckle properties provide additional information of tissue structure, which could help to increase the efficiency of tissue differentiation. The wavelet analysis of OCT speckle patterns was applied to extract the power of local brightness fluctuations in speckle and its standard deviation. The speckle properties are analysed together with attenuation ones using a set of ex vivo brain tissue samples, including glioma of different grades. Various combinations of these features are considered to perform linear discriminant analysis for tissue differentiation. The results reveal that it is reasonable to include the local brightness fluctuations at first two wavelet decomposition levels in the analysis of OCT brain images aimed at neurosurgical diagnosis.

Selection of best wavelet functions and decomposition levels for coupling with soft computing methods in estimating ETo in coastal and island regions

ABSTRACT Mass transfer-based models are among the extensively applied reference evapotranspiration (ET o ) estimation approaches that have been proven to provide reliable estimates under certain climatic and geographical conditions. A major issue with such approaches is the high variations in wind speed time series, which is a governing meteorological parameter in mass transfer-based models. few studies have focused on applying wavelet transform as a robust pre-processing technique for ETo estimation. A major question with coupling wavelet transforms with soft computing methods would be the proper choice of the wavelet function, vanishing moments and the decomposition levels. The present study aims at assessing different wavelet functions coupled with boosted regression tree (BT) models, i.e. wavelet-BT (WBT), in estimating ET o values (through mass transfer parameters) in both coastal and island regions, where it is supposed that wind speed variations are affected by sea–inland interactions and so has the sharp variations (unlike ET o ). The obtained results showed that the coupled WBT model could improve the single BT model results to a great extent, and meanwhile, the Daubechies wavelet function with six vanishing moments provided the most accurate results in all the locations. Further, the best simulation outcomes with each wavelet function were obtained when the maximum possible decomposition level was used with each function.

Multi-Frequency Ultrasound Imaging Fusion Method Based on Wavelet Transform for Guided Screw Insertion.

Intraosseous ultrasound imaging can serve as a guiding tool for the placement of pedicle screws during spinal fusion surgery; thus far, there has been limited scholarly exploration of methods for intraosseous multifrequency ultrasound imaging, which can achieve simultaneous high resolution and deep penetration. The proposed method introduced a dynamic fusion strategy grounded in wavelet transformation for multifrequency image decomposition. This strategy accomplished the effective amalgamation of high-frequency ultrasound images and low-frequency ultrasound images, enabling the obtaining of fused images with enhanced details and better overall image quality. A novel near-field effect elimination method was also proposed to improve the quality of ultrasound imaging in the near-field region. Experimental evaluations were conducted on isolated bovine circle bone and sheep spine with pedicle screw tracks. The fusion images are capable of effectively detecting areas within the pedicle screw track that have either ruptured or are in close proximity to rupture, even measuring the size of breaches. Evaluation criteria, including information entropy (IE), spatial frequency (SF), average gradient (AG), mutual information (MI), structural similarity index (SSIM), and edge information-based image fusion quality metric (QAB/F), were employed to assess the fusion performance; moreover, the influence of mother wavelet function selection and decomposition levels on computational complexity and fusion image quality was thoroughly discussed. The proposed method exhibited promising potential for intraosseous imaging navigation, which can aid in accurate diagnosis, treatment planning, and monitoring in fields such as orthopedics, surgery, and interventional procedures.

ОЦЕНКА ВЛИЯНИЯ КОЭФФИЦИЕНТА МАСШТАБИРОВАНИЯ БАЗОВОЙ ФУНКЦИИ ВЕЙВЛЕТ-ПРЕОБРАЗОВАНИЯ НА СТЕПЕНЬ ПРОЯВЛЕНИЯ ОСНОВНЫХ НЕИСПРАВНОСТЕЙ ЦЕНТРОБЕЖНЫХ НАСОСНЫХ АГРЕГАТОВ В ВЕЙВЛЕТ-КАРТИНАХ

Relevance Rotary-type machines, which include centrifugal pumping units, are widely used in the oil refining and petrochemical industries and represent an integral part of technological processes. Therefore, preventing their emergency failure is the most important task, which is solved using vibroacoustic diagnostics. Vibration diagnostic services of technical supervision departments process signals mainly using the spectral method of vibration signal analysis based on the Fourier transform. Along with the undeniable advantages, which include the simplicity of software implementation and the admissibility of optimization for the analysis of many functions of physical processes, this transformation has certain disadvantages. For example, due to the loss of information about the time factor, the idea of the dynamics of changes in the spectral composition of the signal is distorted, which does not allow for a comprehensive analysis of the vibration signal. In this regard, there is a need for additional methods of digital signal processing. In recent years, in the process of research carried out at the Ufa State Petroleum Technological University, it has been proven that a method based on wavelet transformation of vibration signals can be used to assess the technical condition of pumping and compressor equipment. This type of transformation is capable of recognizing not only periodic components of the signal, but also local ones, determining their time and frequency characteristics, and establishing the relationship between the levels of wavelet decomposition and the frequency ranges of wavelet filters. It has been determined that the level of decomposition during the wavelet transform of the signal can be taken as a criterion for clearing the vibration signal of the digital pump from the noise component in the presence of faults such as «imbalance» and «misalignment». Discrete wavelet transform of vibration signals makes it possible to determine amplitude modulation caused by the manifestation of faults of electromagnetic origin and inhomogeneity of the air flow in the gap between the rotor and stator of an electric motor, as well as to identify slowly developing (trend) signals associated with lubrication defects in the motor bearings of centrifugal pumping units. Wavelet patterns store complex information about the signal, however, when several types of faults or defects are combined, it is very difficult to identify the leading one and the degree of its development, especially in the early stages. In this case, the value of the scaling factor can serve as a characteristic of the degree of development of the fault, since it was found that wavelet patterns begin to differ comprehensively when setting the scaling factor of the wavelet transform of signals, starting from a value of 192, confirming the presence of an anomalous signal. Aim of research Increasing the accuracy of assessing the technical condition of centrifugal pumping units by selecting the scaling factor of the basic function of the wavelet transform of vibration signals. Research methods To practically solve the problems, methods and algorithms for digital processing of vibration signals based on the Fourier transform and wavelet transform were used. Results It has been established that for a more accurate assessment of the stage of development of the main faults of the digital pump using the continuous wavelet transform, it is necessary to use a scaling factor of the basic wavelet function equal to 512.

ОПТИМІЗАЦІЯ АЛГОРИТМУ ПАКЕТНОЇ ВЕЙВЛЕТ-ФІЛЬТРАЦІЇ СИГНАЛІВ

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, after each cycle of processing the wavelet decomposition coefficients, the signal is reconstructed in the time domain. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet-threshold and the threshold function. The study was conducted with twenty of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of packet wavelet filtering, a comparative analysis with the known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. Keywords: wavelet analysis, packet wavelet filtering, entropy, threshold function, threshholding.

A wavelet based PSD approach for fault detection and classification in grid connected inverter interfaced microgrid

The recent progress in the area of microgrid protection has led to the application of data-driven and signal processing techniques for fault detection in microgrids. The deployment of inverter interfaced distributed generators makes the traditional protection schemes ineffective. In this paper a wavelet based power spectral density (PSD) has been utilized to detect fault, identify faulty phases and locate fault in the microgrid. Wavelet based PSD decouples the frequency information from the time information and it is the optimal technique to reveal the change of distribution of harmonics in non-stationary faulty signals as for fault analysis it can consider the faulty frequency band instead of one particular harmonic. The proposed technique can detect fault and identify faulty phases by analyzing current signals from the substation only. The normalized value of PSD of three phase current signals has been considered for fault detection and probabilistic distribution of PSD has been considered for faulty phase identification. The normalized value of PSD of the current signals collected from both ends of the main feeders and one end of the non-DG sub-feeder have been used to locate the faulty feeder and sub-feeder. Appropriate threshold values have been considered to detect fault and to locate the faulty feeder. To locate faults, the technique does not require synchronized signals and thus provides a promising and economical solution for inverter interfaced microgrid. It does not require huge amount of data set for training and testing as it is essentially a threshold based technique and also does not require collection of data at high sampling rate. The proposed scheme has been extensively tested for high impedance fault (HIF), unbalanced loading, load switching, variation of DG parameters, measurement uncertainty and presence of noise in the signal with signal to noise ratio up to 10 dB. This technique provides accurate results for fault resistance from 0 Ω to 300 Ω and up to 10% measurement error. The performance of the proposed technique has been verified for feeder length variation up to 20%. Half cycle of current signal only after fault is required and three levels of wavelet decomposition has been considered. The simulation results and comparative assessment demonstrate the efficacy of the proposed scheme.

Experimental validation of a real-time energy management system using four frequency-based approaches

An innovative approach is introduced in this study for optimizing power distribution within a hybrid energy storage system, which encompasses batteries and supercapacitors. The method involves utilizing an adaptive wavelet technique within the energy management system dedicated to the EV. This technique customizes the wavelet decomposition level based on the supercapacitor's state of charge. As a result, optimal power sharing between the two real sources incorporated in a small-scale EV emulator is achieved. Notably, the approach adjusts the wavelet decomposition level during transient high peaks and when the supercapacitor has high reserves to alleviate battery workload. Through experimental validation and comparative analysis with three other frequency-based techniques, it is demonstrated that the adaptive wavelet control strategy significantly extends battery lifetime. This extension is achieved by reducing the root mean square (RMS) current by 34 % compared to fixed cut-off frequency approaches. Consequently, this minimizes losses and safeguards the battery from high peaks, resulting in a substantial decrease of 44.53 %. These results underscore the substantial potential of the adaptive wavelet approach as a suitable solution for effective energy management in hybrid electric vehicles.

Wavelets in the analysis of local time series of the Earth's surface air

The practical application of local smoothing and wavelet analysis methods for studying the spectral composition and coherent relationships of local average annual surface air temperatures with solar activity and the displacement of the Earth's North Pole is presented. A preliminary analysis of local time series of surface temperatures revealed the presence of emissions and their localization. It is shown that to eliminate the influence of outliers (short-term events) on the reliability of identifying a long-term nonlinear trend, the wavelet decomposition method, which filters high frequencies, is most suitable. Functional approximation models are constructed and compared at different levels of wavelet decomposition of the data. Time or scale smoothing is used to improve the reliability of the wavelet spectrum. Based on data on average annual surface air temperatures in Yalta (44.48⁰, 34.17⁰, = 72.0 m) for the time interval from 1869 to 2022, functional models of long-term trends were built and used to obtain short-term forecasts. Information about the linear relationship of events in the compared time series is obtained and discussed in the analysis of wavelet cross-correlation, wavelet coherence and phase coherence. Local similarities were discovered between data on surface air temperature and solar activity data (Wolf numbers) for a period of ∼(30–70) years, as well as oscillations with period of 11 years, manifested in the constancy of the phase difference and an increase in the modulus of wavelet coherence power over time. Localized similarities were also found in data on surface air temperature in Yalta and in data on displacements of the Earth's mean pole relative to the conventional beginning of EOP (IERS) CO1 in the interval of periods ∼ (30–70) years.

Noise reduction and characteristic analysis of fluid signal in the jet impact‐negative pressure deamination reactor based on wavelet transform

AbstractThe jet impact‐negative pressure deamination reactor (JI‐NPDR) is a new type of continuous and efficient deamination equipment. The study of the random flow pattern of porous jet impingement in the reactor under negative pressure conditions is an important issue. In this work, the signal processing method based on wavelet transform is used to analyze the characteristics of random flow signals in the reactor. Meanwhile, an analog similar signal is built and three sets of Gaussian white noise with various signal‐to‐noise ratios are employed via the MATLAB platform. Based on the adjustment of threshold function, threshold, decomposition level and other parameters of wavelet transform, the noise ratio (SNR) and mean squared error (MSE) are used to evaluate the wavelet denoising effect. And then, the optimal denoising scheme for the obtained signal will be applied in processing the vacuum flow signal collected inside the deamination reactor. Subsequently, the 8‐layer wavelet decomposition is investigated by using sym7 as the wavelet basis, soft threshold function, and heursure threshold for signal denoising. Then, the analog signal is fed back through the results of the actual signal denoising, and the number of wavelet decomposition layers is adjusted from 8 to 9 layers to optimize the original wavelet denoising combination. By analyzing the low‐frequency and high‐frequency parts of the signal spectrum before and after denoising, it was found that wavelet transform can effectively denoise the fluid signal in the reactor.

Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm

PurposeIn real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).Design/methodology/approachIn each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.FindingsResonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.Originality/valueProposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.

METHOD OF LOCAL RESTORATION OF SEGMENTS OF INFORMATION SIGNALS

The use of centralized and decentralized electricity supply schemes, the introduction of feedback between the consumer of electricity and its producer led to a rapid increase in information flows at all stages of the functioning of the electricity industry of Ukraine, starting with the production of electricity and before its consumption. This necessitates the processing, storage and transmission of large data sets. On the other hand, the time constraints imposed on information processing and decision-making efficiency, as well as the limited bandwidth of communication networks require effective optimization of information flows in terms of their compression and compact storage, transmission and recovery without loss. At the same time, the determining quantitative and qualitative information parameters are electricity consumption modes and the quality of electric energy, and the main mode parameter for solving many problems of planning, management and carrying out commercial calculations is the graphs of electric load. Based on the analysis of the functional relationships of wavelet coefficients according to the levels of wavelet decomposition, the robot presents a modified reconstruction scheme and developed a model based on which a method of local (segmental) restoration of information signals according to the levels of wavelet detail is synthesized using the example of the electric load graph. In the paper, a model of local recovery of time segments of information signals is proposed and a sequential algorithm of actions synthesized on its basis. This technique allows for effective segmentation of information signals, reduces the duration of mathematical processing, simplifies database analysis, increases the effectiveness of controlling the reliability of initial data recovery by reserving recovery paths with subsequent comparison of results.

The Effects of Daubechies Wavelet Basis Function (DWBF) and Decomposition Level on the Performance of Artificial Intelligence-Based Atrial Fibrillation (AF) Detection Based on Electrocardiogram (ECG) Signals

This research studies the effects of both Daubechies wavelet basis function (DWBF) and decomposition level (DL) on the performance of detecting atrial fibrillation (AF) based on electrocardiograms (ECGs). ECG signals (consisting of 23 AF data and 18 normal data from MIT-BIH) were decomposed at various levels using several types of DWBF to obtain four wavelet coefficient features (WCFs), namely, minimum (min), maximum (max), mean, and standard deviation (stdev). These features were then classified to detect the presence of AF using a support vector machine (SVM) classifier. Distribution of training and testing data for the SVM uses the 5-fold cross-validation (CV) principle to produce optimum detection performance. In this study, AF detection performance is measured and analyzed based on accuracy, sensitivity, and specificity metrics. The results of the analysis show that accuracy tends to decrease with increases in the decomposition level. In addition, it becomes stable in various types of DWBF. For both sensitivity and specificity, the results of the analysis show that increasing the decomposition level also causes a decrease in both sensitivity and specificity. However, unlike the accuracy, changing the DWBF type causes both two metrics to fluctuate over a wider range. The statistical results also indicate that the highest AF accuracy detection (i.e., 94.17%) is obtained at the Daubechies 2 (DB2) function with a decomposition level of 4, whereas the highest sensitivity, 97.57%, occurs when the AF detection uses DB6 with a decomposition level of 2. Finally, DB2 with decomposition level 4 results in 96.750% for specificity. The finding of this study is that selecting the appropriate DL has a more significant effect than DWBF on AF detection using WCF.

A Bayesian Optimized Variational Mode Decomposition-Based Denoising Method for Measurement While Drilling Signal of Down-the-Hole Drilling

Measurement while drilling (MWD) emerges as a reliable technique for assessing rock mass properties. However, the measured MWD signals are often contaminated with noise, leading to distorted signals. To address this issue, this paper proposes a denoising method that utilizes variational mode decomposition (VMD) and wavelet soft thresholding (WST). The proposed method employs Bayesian optimization to adaptively determine the optimal VMD parameters. The decomposed modes are then further denoised using WST with appropriate thresholding and optimal wavelet decomposition levels. To validate the effectiveness of the proposed method, four synthetic signals with varying input signal-to-noise ratios (SNR) and two sets of measured MWD signals were evaluated. The results demonstrate the surpassing denoising efficiency of the proposed technique in terms of higher output SNR, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and lower RMSE values. Moreover, the denoised MWD signals show promising results, with reduced amplitude and volatility while preserving the characteristics of the original signals.

Optimization of Discrete Wavelet Transform Feature Representation and Hierarchical Classification of G-Protein Coupled Receptor Using Firefly Algorithm and Particle Swarm Optimization

Ineffective protein feature representation poses problems in protein classification in hierarchical structures. Discrete wavelet transform (DWT) is a feature representation method which generates global and local features based on different wavelet families and decomposition levels. To represent protein sequences, the proper wavelet family and decomposition level must be selected. This paper proposed a hybrid optimization method using particle swarm optimization and the firefly algorithm (FAPSO) to choose the suitable wavelet family and decomposition level of wavelet transformation for protein feature representation. The suggested approach improved on the work of earlier researchers who, in most cases, manually selected the wavelet family and level of decomposition based solely on experience and not on data. The paper also applied the virtual class methods to overcome the error propagation problems in hierarchical classification. The effectiveness of the proposed method was tested on a G-Protein Coupled Receptor (GPCR) protein data set consisting of 5 classes at the family level, 38 classes at the subfamily level, and 87 classes at the sub-subfamily level. Based on the result obtained, the most selected wavelet family and decomposition level chosen to represent GPCR classes by FAPSO are Biorthogonal wavelets and decomposition level 1, respectively. The experimental results show that the representation of GPCR protein using the FAPSO algorithm with virtual classes can yield 97.9%, 86.9%, and 81.3% classification accuracy at the family, subfamily, and sub-subfamily levels, respectively. In conclusion, the result shows that the selection of optimized wavelet family and decomposition level by the FAPSO algorithm, and the virtual class method can be potentially used as the feature representation method and a hierarchical classification method for GPCR protein.

Adaptive wavelet pyramid for noisy machinery fault diagnosis with multiple sensors

The fusion of multiple monitoring sensors is crucial to improve the accuracy and robustness of machinery fault diagnosis. However, existing fault diagnosis methods may underestimate the interference of noise in the multi-sensor fusion process, leading to unsatisfied performance. To handle this problem, this paper proposes a deep model based on the frequency adaptive wavelet pyramid. First, an adaptive frequency selection strategy is designed to prune the seriously polluted frequencies and only retain some key frequencies. Then, the self-attention mechanism is used to perform information fusion on the selected frequency bands of different sensors. Finally, a wavelet fusion pyramid is adopted by repeating the fusion process at multiple wavelet decomposition levels. In this way, different sensors can be fused in a more fine-grained manner. The experimental results on two multi-sensor-based fault diagnosis datasets demonstrate the anti-noise capability of the proposed method.

GPCR Protein Feature Representation using Discrete Wavelet Transform and Particle Swarm Optimisation Algorithm

Features play an important role in representing classes in the hierarchy structure, and using unsuitable features will affect classification performance. The discrete wavelet transform (DWT) approach provides the ability to create the appropriate features to represent data. DWT can produce global and local features using different wavelet families and decomposition levels. These two parameters are essential to obtain a suitable representation for classes in the hierarchy structure. This study proposes using a particle swarm optimisation (PSO) algorithm to select the suitable wavelet family and decomposition level for G-protein coupled receptor (GPCR) hierarchical class representation. The results indicate that the PSO algorithm mostly selects Biorthogonal wavelets and decomposition level 2 to represent GPCR protein. Concerning the performance, the proposed method achieved an accuracy of 97.9%, 85.9%, and 77.5% at the family, subfamily, and sub-subfamily levels, respectively.

The effect of the liquid physical properties on the wave frequency and wave velocity of co-current gas-liquid stratified two-phase flow in a horizontal pipe

The aim of the present study was to investigate the effect of the liquid physical properties on the liquid film thickness, wave frequency, and wave velocity in co-current gas-liquid stratified two-phase flow in a horizontal pipe. The present experimental study was conducted using an acrylic pipe with an inner diameter of 26 mm and a length of 9500 mm. The superficial velocity of liquid (JL) and gas (JG) were 0.02 m/s to 0.1 m/s and 4 m/s to 16 m/s, respectively. A highspeed video camera was used to take the visual data which is then processed by the developed image processing techniques to obtain the time series data of the liquid film thickness. The probability distribution function (PDF) and discrete wavelet transform (DWT) were used to analyze the time series of the liquid film thickness. In addition, the data were also analyzed using the power spectral density (PSD) in order to obtain the wave frequency and the wave velocity. Next, the experimental correlations to predict the wave frequency and the wave velocity were developed using the dimensional analysis. From the time series of the liquid film thickness, the effect of the viscosity and surface tension on the shifting of scale and frequency of the wavelet decomposition level, as well as the frequency and velocity of the waves were clarified. In addition, a correlation to predict the frequency and velocity of waves has been successfully developed, in which the Martinelli parameter, the ratio of gas and liquid Reynold numbers, and the Weber number play the important roles in the correlation.

Field measurement analysis of wind parameters and nonstationary characteristics in mountainous terrain: Focusing on cooling windstorms

Cold fronts passing through the mountain areas may produce continuous windstorm and cooling processes, potentially impacting the mountain areas' infrastructure. Cooling windstorms belong to the dynamically-driven wind in the mountain wind system. To accurately estimate the wind field parameters of these storms and provide a basis for structural wind resistance design, cooling windstorms should be extracted and analyzed separately from the wind field observation data. Based on the long-term field measurement in complex mountain terrain, a framework for identifying cooling windstorms is established according to temperature and wind speed features. The mean and fluctuating wind parameters of these intense winds are then obtained. Strong nonstationary is detected for cooling windstorms. This paper focuses on the time-varying regularity of fluctuating parameters during intense wind with cooling based on the evolutionary power spectral density. From the perspective of turbulent energy, the basis for selecting the optimal wavelet decomposition levels is put forward when extracting the time-varying mean wind through discrete wavelet transform in the nonstationary wind speed model. This investigation can provide a reference for studying the nonstationary wind field.