Combining Wavelet Analysis Research Articles

Investigation on the multi-scale interactions in gas–liquid jet bubbling reactor

Due to the unreliability of the mechanical seal of the mechanical stirring reactor in traditional carbonyl synthesis reactions, a gas–liquid jet bubbling reactor has been developed that is a new type of hydraulic stirring. A cold model device was constructed to address the complex flow field characteristics of a gas–liquid jet bubbling reactor, and a gas–liquid phase testing method was established to obtain the gas–liquid phase flow parameters in the cold model device. A mathematical model of a cold model device was established based on computational fluid dynamics. The reliability and accuracy of the calculation model were verified by combining experimental data of the cold model device, and the gas–liquid two-phase flow characteristics of an industrial grade reactor were obtained. The multiscale characteristics of gas–liquid two-phase signals in industrial reactors and the multiscale gas–liquid two-phase interactions were analyzed by combining wavelet analysis, power spectrum analysis, and fractal analysis. Based on the multiscale gas–liquid interaction mechanism model of gas–liquid interaction, the liquid phase interaction in d1-d6 inside the reactor was increased. The gas–liquid mass transfer process was enhanced, and the liquid level fluctuation and temperature difference of industrial grade reactors were significantly reduced.

What Drove the GICs >10 A During the 17 March 2013 Event at Mäntsälä? A Novel Framework for Distinguishing the Magnetospheric Sources

AbstractWe combine wavelet analysis and data fusion to investigate geomagnetically induced currents (GICs) on the Mäntsälä pipeline and the associated horizontal geomagnetic field, BH, variations during the late main phase of the 17 March 2013 geomagnetic storm. The wavelet analysis decomposes the GIC and BH signals at increasing “scales” to show distinct multi‐minute spectral features around the GIC spikes. Four GIC spikes >10 A occurred while the pipeline was in the dusk sector—the first sine‐wave‐like spike at ∼16 UT was “compound.” It was followed by three “self‐similar” spikes 2 hr later. The contemporaneous multi‐resolution observations from ground‐(magnetometer, SuperMAG, SuperDARN), and space‐based (AMPERE, Two Wide‐Angle Imaging Neutral‐atom Spectrometers) platforms capture multi‐scale activity to reveal two magnetospheric modes causing the spikes. The GIC at ∼16 UT occurred in two parts with the negative spike associated with a transient sub‐auroral eastward electrojet that closed a developing partial ring current loop, whereas the positive spike developed with the arrival of the associated mesoscale flow‐channel in the auroral zone. The three spikes between 18 and 19 UT were due to bursty bulk flows (BBFs). We attribute all spikes to flow‐channel injections (substorms) of varying scales. We use previously published MHD simulations of the event to substantiate our conclusions, given the dearth of timely in‐situ satellite observations. Our results show that multi‐scale magnetosphere‐ionosphere activity that drives GICs can be understood using multi‐resolution analysis. This new framework of combining wavelet analysis with multi‐platform observations opens a research avenue for GIC investigations and other space weather impacts.

Transmission Line Fault Classification Based on the Combination of Scaled Wavelet Scalograms and CNNs Using a One-Side Sensor for Data Collection.

This research focuses on leveraging wavelet transform for fault classification within electrical power transmission networks. This study meticulously examines the influence of various parameters, such as fault resistance, fault inception angle, fault location, and other essential components, on the accuracy of fault classification. We endeavor to explore the interplay between classification accuracy and the input data while assessing the efficacy of combining wavelet analysis with deep learning methodologies. The data, sourced from network recorders, including phase currents and voltages, undergo a scaled continuous wavelet transform (S-CWT) to generate scalogram images. These images are subsequently utilized as inputs for pretrained deep learning models. The experiments encompass various fault scenarios, spanning distinct fault types, locations, times, and resistance values. A remarkable feature of the proposed work is the attainment of 100% classification accuracy, obviating the need for additional algorithmic enhancements. The foundation of this achievement is the deliberate selection of the right input. The decision to employ an identical number of samples as the number of scales for the CWT emerges as a pivotal factor. This approach underpins the high accuracy and renders supplementary algorithms superfluous. Furthermore, this research underscores the versatility of this approach, showcasing its effectiveness across diverse networks and scenarios. Wavelet transform, after rigorous experimentation, emerges as a reliable tool for capturing transient fault characteristics with an optimal balance between time and frequency resolutions.

Comparative Analysis of Artificial Neural Network (ANN) and Wavelet Integrated Artificial Neural Network (W-ANN) Approaches for Rainfall Modeling of Southern Rajasthan, India

This paper addresses the challenge of predicting erratic rainfall in Rajasthan state of India, particularly in southern regions. Reliable rainfall predictions are crucial for water resource management and agriculture planning. The research involved selecting 58 stations across seven districts of southern Rajasthan and identifying the best fit computational neural (ANN) and wavelet integrated computational neural (W-ANN) architectures based on performance metrics. Different combinations of input characters, hidden layer neurons, learning algorithms, and training cycles were tested to determine optimal models. Hybrid models, combining wavelet analysis with ANN, were explored to tackle non-stationary hydrologic signals effectively. Results showed that ANN Model C with ten input layer neurons performed best for 74% of stations, followed by Model B (21% of stations) and Model A (5% of stations). Models with increased input and hidden layer neurons performed better. Among the selected stations, 81% of stations demonstrated improved performance using W-ANN models due to effective signal decomposition and information extraction. The hybrid W-ANN models outperformed simple ANN models for rainfall prediction. Both ANN and W-ANN models accurately forecasted weekly rainfall, as observed in the comparison of actual and forecasted values.

Two-Step Identification Method and Experimental Verification of Weld Damage at Joints in Spatial Grid Structures

Welded joints in grid structures are susceptible to damage and destruction when exposed to random excitation. The complexity of the grid structure poses challenges for realizing the damage recognition of welded joints. In this study, a two-step method is proposed specifically for damage identification of welded joints in grid structures, combining wavelet analysis and fuzzy pattern recognition to accurately identify the location and extent of damage in welded joints. Firstly, the structure is divided based on the analysis of the influence range of joint damage. Key joints are selected within the sub-regions where sensors are installed, and the acceleration response of these key joints is measured. Wavelet analysis is then applied to identify the sub-regions where weld damage occurs. Secondly, an equivalent finite element model is established for joints with varying degrees of damage. The damage index, calculated as the ratio of the absolute value of the difference in the first-order element strain mode of the members, increases with the degree of damage during joint weld damage. By monitoring the changes in the damage index of sensitive members, which exhibit significant changes with varying weld damage degrees, a damage pattern database is constructed for each sub-region. The membership degree between joint damage and the patterns in the pattern database is then calculated to determine the location and degree of weld damage. To validate the effectiveness of the proposed method, an experiment was conducted using a grid structure model with replaceable members. Highly sensitive FBG sensors were designed to measure the acceleration response of the joints, resulting in accurate identification of damaged sub-regions solely through the measurement of key joint acceleration responses. Furthermore, within the damaged sub-regions, the fuzzy pattern recognition method precisely determined the location and degree of weld damage in the joints. The experimental results demonstrate that the proposed method effectively reduces the complexity of the structure by dividing the grid structure into sub-regions, and enables the two-step identification method to achieve successful damage identification for the joints in the grid structure with high efficiency and accuracy.

Association and driving factors of meteorological drought and agricultural drought in Ningxia, Northwest China

Under global warming, drought problems have become increasingly prominent, which has seriously affected the ecological environment's protection and social and economic development at global and regional scales. Ningxia is an arid region in northwest China with serious water problems, and droughts further exacerbate its water security and hinder ecological and socio-economic development. Therefore, this study explored the temporal and spatial distribution characteristics of meteorological and agricultural droughts and their driving factors in Ningxia during 2002–2021 by combining wavelet analysis and grey relational analysis. The main conclusions are as follows: (1) precipitation, soil moisture (SM), and evapotranspiration (ET) in Ningxia increased significantly, while the main meteorological drought events in Ningxia appeared around 2006, 2011, and 2015, and the agricultural drought first became stronger and then weaker; (2) precipitation and ET were correlated with meteorological drought in Ningxia, with a coefficient above 0.8, while the correlation between agricultural drought and precipitation, ET, and gross primary production (GPP) were very significant; and (3) precipitation, ET, and GPP were not all included in the drivers of meteorological drought in Ningxia, whereas agricultural drought had a grey correlation with precipitation, ET, and GPP according to the grey relational analysis. This study is of great significance for revealing the spatiotemporal characteristics and driving factors of drought in Ningxia as well as the early warning and risk management.

TSDNet: A New Multiscale Texture Surface Defect Detection Model

Industrial defect detection methods based on deep learning can reduce the cost of traditional manual quality inspection, improve the accuracy and efficiency of detection, and are widely used in industrial fields. Traditional computer defect detection methods focus on manual features and require a large amount of defect data, which has some limitations. This paper proposes a texture surface defect detection method based on convolutional neural network and wavelet analysis: TSDNet. The approach combines wavelet analysis with patch extraction, which can detect and locate many defects in a complex texture background; a patch extraction method based on random windows is proposed, which can quickly and effectively extract defective patches; and a judgment strategy based on a sliding window is proposed to improve the robustness of CNN. Our method can achieve excellent detection accuracy on DAGM 2007, a micro-surface defect database and KolektorSDD dataset, and can find the defect location accurately. The results show that in the complex texture background, the method can obtain high defect detection accuracy with only a small amount of training data and can accurately locate the defect position.

Wavelet-based fuzzy clustering of interval time series

We investigate the fuzzy clustering of interval time series using wavelet variances and covariances; in particular, we use a fuzzy c-medoids clustering algorithm. Traditional hierarchical and non-hierarchical clustering methods lead to the identification of mutually exclusive clusters whereas fuzzy clustering methods enable the identification of overlapping clusters, implying that one or more series could belong to more than one cluster simultaneously. An interval time series (ITS) which arises when interval-valued observations are recorded over time is able to capture the variability of values within each interval at each time point. This is in contrast to single-point information available in a classical time series. Our main contribution is that by combining wavelet analysis, interval data analysis and fuzzy clustering, we are able to capture information which would otherwise have not been contemplated by the use of traditional crisp clustering methods on classical time series for which just a single value is recorded at each time point. Through simulation studies, we show that under some circumstances fuzzy c-medoids clustering performs better when applied to ITS than when it is applied to the corresponding traditional time series. Applications to exchange rates ITS and sea-level ITS show that the fuzzy clustering method reveals different and more meaningful results than when applied to associated single-point time series.

Combining wavelet analysis of track irregularities and vehicle dynamics simulations to assess derailment risks

Guaranteeing operational safety is mandatory for railways worldwide. As track deteriorates, its geometry deviates from ideal conditions (e.g. perfectly aligned and levelled), which creates undesired vibration and oscillations to the vehicle, increasing dynamic loads and derailment risk. Although current standards establish nominal limits for the track geometry, such point-wise comparisons may overlook relevant track features that can lead to unsafe conditions. The proposed investigation is a contribution to the study of the response of the rail vehicle to the track quality, aimed at identifying track irregularities that produce high track forces and unsafe vehicle responses. To fulfil this aim, Wavelet Analysis is combined with Vehicle Dynamics Simulations to evaluate how the track irregularities, filtered in various wavelength ranges and reconstructed with different wavelets and coefficients' amplitudes, impact vehicle safety in terms of the Nadal safety criterion Y/Q. The simulations demonstrate that defects occurring in some scales/frequencies are more harmful than others, and the similarity between the geometric defects and the shape of the wavelets may be used to identify track locations that require maintenance. These findings suggest that it is possible to create ‘stamps’ of track irregularities that can be used by infrastructure managers to improve their maintenance strategies.

Harmonic Analysis and Self-Tuning Control Combining Wavelet Analysis and Identification for High-Tc RF SQUID

High-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> radio-frequency (rf) superconducting quantum interference devices are well understood and widely used in many areas of low-field measurement because of their high sensitivity and high resolution. Harmonic analysis has proven to be an efficient way for finding the optimum working point. However, there is a precondition for using harmonic analysis, which is not well understood so far. In this article, it is shown that the precondition can be fulfilled in the typical range of parameters and under our experimental conditions by using a direct mathematical derivation. It is demonstrated that the improvement of wavelet analysis in mean square error (MSE) is more than 50% for harmonic analysis. In addition, identification by forgetting factor recursive least square is a helpful way for self-tuning controller who gives fast tracking, small MSE and high coefficient of determination (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) for harmonic analysis of different experimentally measured signals.

Surface Rotation and Photometric Activity for Kepler Targets. II. G and F Main-sequence Stars and Cool Subgiant Stars

Abstract Dark magnetic spots crossing the stellar disk lead to quasiperiodic brightness variations, which allow us to constrain stellar surface rotation and photometric activity. The current work is the second of this series, where we analyze the Kepler long-cadence data of 132,921 main-sequence F and G stars and late subgiant stars. Rotation-period candidates are obtained by combining wavelet analysis with autocorrelation function. Reliable rotation periods are then selected via a machine-learning (ML) algorithm, automatic selection, and complementary visual inspection. The ML training data set comprises 26,521 main-sequence K and M stars from Paper I. To supplement the training, we analyze in the same way as Paper I, i.e., automatic selection and visual inspection, 34,100 additional stars. We finally provide rotation periods P rot and associated photometric activity proxy S ph for 39,592 targets. Hotter stars are generally faster rotators than cooler stars. For main-sequence G stars, S ph spans a wider range of values with increasing effective temperature, while F stars tend to have smaller S ph values in comparison with cooler stars. Overall for G stars, fast rotators are photometrically more active than slow rotators, with S ph saturating at short periods. The combined outcome of the two papers accounts for average P rot and S ph values for 55,232 main-sequence and subgiant FGKM stars (out of 159,442 targets), with 24,182 new P rot detections in comparison with McQuillan et al. The upper edge of the P rot distribution is located at longer P rot than found previously.

Changes in blood–brain barrier permeability characterized from electroencephalograms with a combined wavelet and fluctuation analysis

Changes in blood–brain barrier permeability characterized from electroencephalograms with a combined wavelet and fluctuation analysis

On the spatiotemporal complementarity of the European onshore wind resource

Among the renewable energy sources, the highest share of European net electricity generation comes from wind power. However, the European onshore wind resource’s volatile nature is a significant challenge in ensuring a constant national electricity supply. Therefore, this study examined the potential of complementary use of national wind resources available in 33 European countries. The complementarity of the national wind resources was assessed for 1971–2010 by identifying the time scales explaining the largest part of the variance in the time series of daily wind energy yield. The results of a novel combination of wavelet analysis, graph models, and dynamic time warping indicate that the wind energy yield shows the most substantial variations at the annual, seasonal, and multi-day scales. Geographical proximity is a critical factor in the complementarity of national wind energy yields. At all evaluated time scales, the wind energy yield in most central and western European countries is strongly correlated, forming a large supranational network with low potential for complementary use of national wind resources. Although the seasonal component of daily wind energy yield is shifted between the European countries by up to several weeks, which would create potential for complementary use, domestic electricity consumption often exceeds the usable wind resources. Domestic electricity consumption was found to be a major barrier to the transboundary exchange of wind energy. Based on the results obtained for the European onshore wind resource’s spatiotemporal dynamics, it must be assumed that the potential for regular complementary transboundary use of wind resources is limited.

Multi-scale flood prediction based on GM (1,2)-fuzzy weighted Markov and wavelet analysis

Abstract In order to forecast flood accurately and reveal the relationship between rainstorm and flood at the micro level, a model which combines wavelet analysis, GM (1,2) and fuzzy weighted Markov is built. Taking the Jialu River of Zhengzhou City in China as study area, the GM (1,2) model is constructed between the components of rainfall and flood volume by wavelet decomposition to connect the two variables, then a fuzzy weighted Markov method is introduced to correct the predicted component of flood volume. The corrected results are superimposed to obtain the predicted value of flood. To verify the reliability of the model, the maximum daily, 3-, 5- and 7-day flood volume of the next five floods in Zhongmu and Jiangang hydrological stations are predicted in turn. The results show that the multi-scale flood forecasting model has high overall forecasting accuracy, with the average relative errors all less than 10%. The forecasting accuracy of maximum five-day flood volume is higher than other periods. On the micro level, the results indicate that the fluctuation trend and period of rainfall-flood volume in d1, d2 and d3 are basically the same. Among the components of forecasted flood, the impact of rainfall on flood volume is most significant in the d3 component.

Intelligent Fault Diagnosis of Hydraulic Piston Pump Based on Wavelet Analysis and Improved AlexNet.

Hydraulic piston pump is the heart of hydraulic transmission system. On account of the limitations of traditional fault diagnosis in the dependence on expert experience knowledge and the extraction of fault features, it is of great meaning to explore the intelligent diagnosis methods of hydraulic piston pump. Motivated by deep learning theory, a novel intelligent fault diagnosis method for hydraulic piston pump is proposed via combining wavelet analysis with improved convolutional neural network (CNN). Compared with the classic AlexNet, the proposed method decreases the number of parameters and computational complexity by means of modifying the structure of network. The constructed model fully integrates the ability of wavelet analysis in feature extraction and the ability of CNN in deep learning. The proposed method is employed to extract the fault features from the measured vibration signals of the piston pump and realize the fault classification. The fault data are mainly from five different health states: central spring failure, sliding slipper wear, swash plate wear, loose slipper, and normal state, respectively. The results show that the proposed method can extract the characteristics of the vibration signals of the piston pump in multiple states, and effectively realize intelligent fault recognition. To further demonstrate the recognition property of the proposed model, different CNN models are used for comparisons, involving standard LeNet-5, improved 2D LeNet-5, and standard AlexNet. Compared with the models for contrastive analysis, the proposed method has the highest recognition accuracy, and the proposed model is more robust.

Analysis of Landscape Ecological Planning Based on the High-Order Multiwavelet Neural Network Algorithm.

Landscape architecture has both natural and social properties, which is the embodiment of people protecting the natural environment. Since the industrial revolution, the modern industry has developed rapidly. It has increased the living standard of people and consumed a lot of natural resources such as forest and energy. The ecological environment has been greatly damaged, and the landscape of gardens has been affected. Therefore, it is of great significance to find a method to evaluate the landscape ecology and plan the landscape ecology. This paper proposes a new high-order wavelet neural network algorithm combining wavelet analysis and artificial neural network. A model of ecological evaluation of landscape based on high-order wavelet neural network algorithm is proposed to evaluate the landscape ecology and provide reference data for the ecological planning of the landscape. The results show that the training times of the wavelet neural network to achieve the target accuracy are 3600 times less than those of the BP neural network. The MSE and MAE of the WNN are 0.0639 and 0.1501, respectively. The average error of the model to the comprehensive evaluation index of the landscape ecology is 0.005. The accuracy of the model to evaluate the sustainability of landscape land resources is 98.67%. The above results show that the model based on the wavelet neural network can effectively and accurately complete the evaluation of landscape ecology and then provide a decision-making basis for landscape ecological planning, which is of high practicability.

A new prediction method of seafloor hydrothermal active field based on wavelet neural network

The study of modern seafloor hydrothermal activity and its mineralization has become one of the focuses of global geoscience. Accurate prediction of possible seafloor hydrothermal active fields is the basis of all research work. The detecting method for new seafloor hydrothermal activity still is mainly dependent on marine site investigation. This includes a series of temperature, turbidity, and geochemical anomaly investigations using submarine cameras and manned diving investigation. Both of these require expensive financial, human, and material resources. In order to realize the accurate prediction of potential hydrothermal activity areas in a low cost manner, with strong pertinence, and a wide range, we propose a prediction method of seafloor hydrothermal active region based on Wavelet Neural Network. First, we integrated the hydrothermal position information from the InterRidge Vents Database with the hydrothermal temperature information form the Argo Database to construct a data set. Then, we combined wavelet analysis with an artificial neural network to create a wavelet neural network optimization algorithm. Finally, the temperature and salinity data were input to the wavelet neural network to predict the seafloor hydrothermal active region. Sevenfold cross validation was used to evaluate the performance of the model and 90.43% prediction accuracy was achieved. The results of experiments show that salinity is not related to the existence of hydrothermal activity fields but rather that the surrounding water temperature has a strong correlation with hydrothermal existence. Therefore, it is effectively feasible to use the wavelet neural network model with an input of seawater temperature to predict seafloor hydrothermal activity fields. Although artificial neural network cannot completely replace traditional hydrothermal exploration technology, it can provide a valuable reference with a strong target.

Wavelet periodic and compositional characteristics of atmospheric PM2.5 in a typical air pollution event at Jinzhong city, China

To investigate the contributions of atmospheric particulate matter less than 2.5 μm in aerodynamic diameter (PM2.5) to heavy air pollution events in Fen-Wei Plain, China and identify their sources, a combination of wavelet analysis and low-atomic number (Z) particle electron probe X-ray microanalysis (EPMA) was utilized in a typical haze episode lasting 10 days (from Nov. 11 to 20, 2016) at Jinzhong, an inland city adjacent to Taiyuan, the capital of Shanxi Province. A 3-layer wavelet decomposition filtration was performed using the daubechies wavelet functions (db6) and the distribution of the real wavelet transformation coefficients and variance of wavelet series for various pollutants within 240 h was plotted. Five dominant periods of PM2.5 in mass concentration were observed, peaking at 101 h, 144 h, 50–51 h, 27–28 h, and 18 h in sequence from high to low in the wavelet variance chart. They were similar to those of PM10, SO2, and CO and partially overlapped with those of NO2, but different from those of O3, implying that PM2.5 have the same sources as PM10, SO2, and CO and have complicated relations with O3 and NO2. It was further found that the chemical compositions of PM2.5 in the dominant periods made great changes compared to the non-dominant periods. The relative number abundance of elemental carbon (EC) and droplets rich in CNOS (likely the mixture of carbonaceous matter with secondary aerosols such as NH4NO3 and (NH4)2SO4/NH4HSO4) in the first and second dominant period were significantly higher than that in other periods. It is concluded that coal and biomass combustion and secondary particles are still the main contributors to the wintertime heavy air pollution events in Fen-Wei Plain, suggesting that the wavelet analysis combined with low-Z particle EPMA is useful in examination of atmospheric particulate matter's origin, evolution, and roles played in haze events.

China's liberalizing stock market, crude oil, and safe-haven assets: A linkage study based on a novel multivariate wavelet-vine copula approach

China is the world's largest oil importer, and therefore the correlations between stock indices and highly volatile oil prices deserve close examination when investing in China's gradually liberalizing stock market. Another concern for international investors is whether safe-haven assets can reduce portfolio risks for investment in China. The paper makes two main contributions. First, we develop a novel method of examining a multivariate dependence structure by combining wavelet analysis with the vine copula model. Second, we apply the proposed methodology to study the correlations between China's liberalizing stock market, petroleum, and safe-haven assets at different frequencies. We find that the multidimensional dependence of these assets has been altered as a result of the 2008 global financial crisis. Moreover, the vine structures exhibit dependence patterns that vary over time horizons, indicating that the multidimensional dependence is sensitive to time scales.

Monthly Precipitation Forecasts Using Wavelet Neural Networks Models in a Semiarid Environment

Accurate forecast of hydrological data such as precipitation is critical in order to provide useful information for water resources management, playing a key role in different sectors. Traditional forecasting methods present many limitations due to the high-stochastic property of precipitation and its strong variability in time and space: not identifying non-linear dynamics or not solving the instability of local weather situations. In this work, several alternative models based on the combination of wavelet analysis (multiscalar decomposition) with artificial neural networks have been developed and evaluated at sixteen locations in Southern Spain (semiarid region of Andalusia), representative of different climatic and geographical conditions. Based on the capability of wavelets to describe non-linear signals, ten wavelet neural network models (WNN) have been applied to predict monthly precipitation by using short-term thermo-pluviometric time series. Overall, the forecasting results show differences between the ten models, although an effective performance (i.e., correlation coefficients ranged from 0.76 to 0.90 and Root Mean Square Error values ranged from 6.79 to 29.82 mm) was obtained at each of the locations assessed. The most appropriate input variables to obtain the best forecasts are analyzed, according to the geo-climatic characteristics of the sixteen sites studied.