Combining Wavelet Analysis Research Articles

Characteristics and Causes of Long-Term Water Quality Variation in Lixiahe Abdominal Area, China

The Lixiahe abdominal area is a representative plain river network in the lower reaches of the Huai River, being an upstream section of south-to-north water diversion from the Yangtze River in Jiangsu Province, China. The assessment of long-term water quality variation and the identification of probable causes can provide references for sustainable water resources management. Based on the monthly water quality data of 15 monitoring stations in the Lixiahe abdominal area, the periodic characteristics and tendency of water quality variation were studied by combining wavelet analysis, the Mann–Kendall trend test, and Sen’s slope estimator, and the correlation between water quality variation, water level, and water diversion was discussed with cross wavelet transform and wavelet coherence. The results show that the comprehensive water quality index (CWQI) included periodic fluctuations on multiple scales from 0.25 to 5 years. The CWQI of 7 out of 15 monitoring stations has a significant decreasing trend, indicating regional water quality improvement. The trend slope ranges from −0.071/yr to 0.007/yr, where −0.071/yr indicates the water quality improvement by one grade in 15 years. The spatial variation of water quality in the Lixiahe abdominal area was significant. The water quality of the main water diversion channels and its nearby rivers was significantly improved, while the improvement of other areas was not significant or even became worse due to the increasing discharge of pollutants. The CWQI of the main water diversion channels and its nearby rivers was inversely correlated with the amount of water diversion. The greater the amount of water diversion, the better the water quality. The water diversion from the Yangtze River has played an important role in improving the regional water environment.

Fault Diagnosis Scheme Based on Microbial Fuel Cell Model

Around the world, fossil fuels are decreasing and pollution is increasing. As a new energy source, microbial fuel cells (MFCs) have been widely concerned. However, most of the previous researches focused on the material selection, configuration design and optimal control of MFCs, and few of them were able to systematically analyze the failures of MFCs. In order to ensure the reliable operation of MFCs, this paper systematically explores the MFC fault diagnosis process, including the acquisition of initial fault data, feature extraction and fault classification.Firstly, in order to acquire data quickly and effectively, the mathematical model is used to simulate the occurrence of faults, and four types of typical fault voltages are obtained. Then, wavelet analysis is used to extract the voltage characteristics of MFC faults, and the characteristics of each fault are explored in eight frequency bands. Finally, the recognition effects of various classifiers on fault features are compared. Through the analysis of the results, it is found that fault tree is the most suitable fault diagnosis method for MFCs. The fault data extraction method proposed in this paper and the classification effect of various classifiers finally obtained provide a reference for the further analysis of MFC faults.At the same time, the combination of wavelet analysis and fault tree diagnosis model proposed in this paper provides ideas for fault diagnosis in other fields.

Stream of Unbalanced Medical Big Data Using Convolutional Neural Network

In order to address the problem that the traditional algorithm can not predict the network link load effectively, which leads to high packet loss and energy loss, long turnaround time, slow stream rate and poor anti-attack ability, the paper proposes the stream algorithm of unbalanced medical big data based on convolutional neural network (CNN). The proposed algorithm included two stages:In the first stage, the decomposition-prediction model was constructed, the combined wavelet analysis and neural network analysis were used to complete the network link load prediction; In the second stage, based on the network link load situation, we analyzed the structure of each layer of convolution neural network, constructed the medical big data stream optimization model, introduced the ReLu function to calculate the convolution neural network, solved the optimization model, and completed the stream processing of unbalanced medical big data. The experimental results show that the network link load prediction accuracy of the proposed stream algorithm is as high as 93%, the lowest packet loss rate is only 2.0%, the energy loss of the stream process is low, the rate is fast, and the anti-attack efficiency is high, which is more conducive to the realization of data stream.

Distribution mapping of soil profile carbon and nitrogen with laboratory imaging spectroscopy

Conversion of arable cropland to forage crops has been proposed as a potential method to increase soil organic carbon (SOC) stocks to sequester carbon and improve soil quality. In this study, intact soil cores were collected from long-term boreal forest soil research plots established in 1980 consisting of: a mixed arable crop and forage agroecological rotation (AE), continuous forage (CF), and continuous grain (CG) rotations. These cores were analyzed using a SisuROCK automated hyperspectral imaging system in a laboratory setting collecting shortwave infrared reflectance data. Samples were then analyzed for SOC and total nitrogen (TN) contents by dry combustion to prepare a training data set. Predictive models were successfully built for SOC and TN using a combination of wavelet analysis and Bayesian Regularized Neural Nets. The CF rotation was found to have the highest SOC and TN contents compared to AE rotation for only the top 3 and 4 cm, respectively. These two rotations had comparable contents for both parameters for the rest of the topsoil, which was greater than the SOC and TN contents in the CG rotation to depths of approximately 12 cm. Increases in both SOC and TN were associated with increased spatial aggregation at fine spatial scales. These results indicate that adding forages to rotations in boreal forest soils increases SOC and TN, however these changes were concentrated in the surface depths.

Precision fertilization method of field crops based on the Wavelet-BP neural network in China

Abstract In the process of agricultural production, the yield of field crops is affected by the interaction of various factors. This relationship between soil nutrients, fertilization, and yield is very complicated. It has strongly non-linear and black box characteristics and is difficult to quantify with traditional analytic methods. This paper proposes a method for the precision fertilization of maize based on the wavelet-BP neural network. Firstly, the existing “3414″ experimental data was chosen and interpolated as the performing data for the modeling. Then, the general condition of low frequency and details of high-frequency of the yield were calculated via the wavelet decomposition and reconstruction method. After that, the wavelet-BP neural network was established. Three different BP neural sub-networks for each component of the yield after wavelet analysis were established, and the output of each sub-network was summed to obtain the predicted corn yield. The results show that the model that combines wavelet analysis with the BP neural network achieves better performance than the traditional BP neural network, Support Vector Machine (SVM), and Random Forest regarding accuracy and stability, which indicates the feasibility of this method. Finally, the best fertilizer amount that achieves the maximum yield or maximum profit is calculated based on nonlinear programming. The proposed method of the wavelet-BP neural network provides a new technique for precision fertilization research and enriches the existing fertilization system. The application of precision fertilization based on the wavelet-BP neural network has important practical significance that guides and increases maize production, while reducing production cost and agricultural pollution. At the same time, it also provides a way to solve similar problems in the entire field of cleaner agricultural production.

Crack detection in rotating shafts using combined wavelet analysis

There are many rotating mechanical systems on board ships that comprise the main shaft transmission element. Proper functioning of shafts depends on many factors: alignment system, connections with other elements - couplings, gearboxes, bearing elements with ball bearings or bushings, operated regime, and al. All these factors can lead to fatigue of the shaft over time and to appearance of internal/external cracks which can determine a total damage of the shaft at some point in time. To avoid these disasters the operation of these rotating systems is monitored based on vibration analysis of recorded signals (FFT and DFT analysis). Due to the transient modes and the presence of the noise, the processing of the recorded signals must be performed with methods that present a good resolution simultaneously in the time and frequency domain. In the paper, measurements are made on a stand with a rotating system and it is determined the influence of some factors (measuring points and directions, speed, operated mode, crack size, presence of misalignment, noise) on the quality of the Wavelet Transform results. In order to improve the clarity of amplitudes and frequencies changes at the initiation of shaft cracks, the authors are proposing the combined use of Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT) and Wavelet Packet Transform (WPT). The authors propose using power spectral density (PSD) as it is a method with good performance in detecting faults in rotating machines.

Detection of correlation characteristics between financial time series based on multi-resolution analysis

Interactions between financial time series are complex and changeable in both time and frequency domains. To reveal the evolution characteristics of the time-varying relations between bivariate time series from a multi-resolution perspective, this study introduces an approach combining wavelet analysis and complex networks. In addition, to reduce the influence the phase lag between the time series has on the correlations, we propose dynamic time-warping (DTW) correlation coefficients to reflect the correlation degree between bivariate time series. Unlike previous studies that symbolized the time series only based on the correlation strength, the second-level symbol is set according to the correlation length during the coarse-graining process. This study presents a novel method to analyze bivariate time series and provides more information for investors and decision makers when investing in the stock market. We choose the closing prices of two stocks in China’s market as the sample and explore the evolutionary behavior of correlation modes from different resolutions. Furthermore, we perform experiments to discover the critical correlation modes between the bull market and the bear market on the high-resolution scale, the clustering effect during the financial crisis on the middle-resolution scale, and the potential pseudo period on the low-resolution scale. The experimental results exactly match reality, which provides powerful evidence to prove that our method is effective in financial time series analysis.

Detecting dynamic spatial correlation patterns with generalized wavelet coherence and non-stationary surrogate data

Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to detect short-lived spatial coherent patterns from multivariate time-series. In contrast with standard methods, the surrogate data proposed here are realisations of a non-stationary stochastic process, preserving both the amplitude and time-frequency distributions of original data. We evaluate this framework on synthetic and real-world time series, and we show that it can provide useful insights into the time-resolved structure of spatially extended systems.

The Effect of Manual Wheelchair Propulsion Speed on Users' Shoulder Muscle Coordination Patterns in Time-Frequency and Principal Component Analysis.

A rehabilitation program for wheelchair users should be based on a thorough understanding of shoulder muscle coordination patterns. The objective of the study was to quantify the extent to which the muscle electromyographic (EMG) patterns vary with propulsion speed. A total of 11 wheelchair-dependent participants with a diagnosis of spina bifida or T6-T12 spinal cord injury volunteered for the study. Each participant performed a series of wheelchair propulsion bouts at 1m/s, 1.3 m/s, and 1.6m/s. EMG signals of 8 shoulder muscles as well as the physiological and kinetic variables were recorded. Propulsion at 1.6m/s generated significantly higher EMG intensities in biceps brachii, anterior deltoid, pectoralis major, and middle deltoid than at 1m/s and 1.3m/s. The combined wavelet and principal component analysis showed that the faster propulsion speed requires higher push muscle activity in the early push phase and in the phase transitions between alternating push and recovery. Training to strengthen the shoulder flexors to achieve smoother phase transitions could improve rehabilitation outcomes by increasing functional speed while lessening shoulder strain.

Research on Fault Diagnosis Method of Electric Vehicle Battery System Based on Wavelet-RBF Neural Network

Combining the good pattern recognition performance of neural network and the data processing performance of wavelet decomposition, this paper combines wavelet analysis with neural network and uses particle swarm optimization radial basis function neural network to diagnose the fault of electric vehicle battery. In this paper, for large data volume and redundant data, wavelet decomposition is used to process signal processing, including data noise reduction and feature vector extraction. In the fault diagnosis of electric vehicle battery system, a radial basis function RBF neural network based on particle swarm optimization (PSO) optimization is proposed. Finally, the reliability and feasibility of the proposed algorithm are proved by simulation.

Multi-Scale Principal Component Analysis for the Fault Detection and Isolation in Induction Motors

Induction motors, though rugged, undergo faults due to wear and tear in their operation. Some faults have the characteristic property of influencing the stator current frequencies. Some side-band frequencies can be observed in the case of such faults. In this paper, a Multi-Scale Principal Component Analysis which combines wavelet analysis with principal component analysis has been applied to the data obtained from the simulation model of an induction motor. A 3-level decomposition of the data is performed and the principal component analysis is applied to high-frequency and low-frequency components of the data at various levels. The results suggest the use of the scheme for timely detection and identification of the faults which would endanger the motor from the otherwise possible destruction. It has also been proved that the scheme has the capability of detecting the sensor faults also, in addition to the motor faults.

Temporal dynamics of subsurface soil water content estimated from surface measurement using wavelet transform

Temporal variation of water in the vadose zone is important to understand processes such as solute transport and nutrient cycling. Measurements of soil water content (SWC) in the subsurface are less common than those near the surface and predictions using numerical models are limited by data availability. Wavelet decomposition of surface measurements of SWC could improve modeling of subsurface SWC by segregating features at different temporal scales and projecting them to the subsurface. The objectives of this work were to: 1) predict subsurface SWC using surface SWC and a combination of wavelet analysis and linear regression, and 2) investigate relationships between soil properties and the movement of soil water at various temporal scales, s. Climate data and SWC at various depths were collected from eight sites in the Atlantic Coastal Plain of the USA. Soil water retention and hydraulic conductivity (k) functions of each horizon were optimized by comparing measured and predicted (using HYDRUS-1D) soil water contents. Each time series of SWC was decomposed into 50 scale components using the Mexican Hat wavelet and later reduced to 5 group components with minimal impact on the characteristics of the signal. Changes in the values of each group component with depth were represented with transfer coefficients that could be estimated with predictors derived from particle size distributions and optimized soil hydraulic functions. Prediction depth and saturated k were the two most important predictors for s < 256 h, while k at −10 kPa was the best predictor for 256 h < s < 724 h, and the median value of particle size diameters for s > 724 h. Subsurface soil water content can be reasonably predicted with the proposed approach, particularly when vertical movement of soil water is unrestricted.

Determinants of dependence structures of sovereign credit default swap spreads between G7 and BRICS countries

We investigate the time-varying dependence structures between G7 and BRICS countries' sovereign credit default swap (CDS) spreads for different timescales by combining wavelet analysis and the copula approach. First, by employing wavelet analysis, we find increasing dependence between the G7 and BRICS's CDS spreads with a decreasing significance level as the timescale increases. Second, the CDS spread dependence across most timescales is better described by the time-varying, than the time-invariant, copulas. Third, gold served as a risk-haven asset may play a good indicator to measure the sovereign credit risk, as well as its dependence. Additionally, the CDS spreads for both G7 and BRICS countries behave simultaneously when the economy is prosperous, but not for the economic depression period. Finally, from the regression of the wavelet components, we find no significant results for the short-term wavelets, whereas significant results are present for both the middle- and long-term scales.

Wavelet regression: An approach for undertaking multi-time scale analyses of hydro-climate relationships

Previous studies showed that hydro-climate processes are stochastic and complex systems, and it is difficult to discover the hidden patterns in the and non-stationary data and thoroughly understand the hydro-climate relationships. For the purpose to show multi-time scale responses of a hydrological variable to climate change, we developed an integrated approach by combining wavelet analysis and regression method, which is called wavelet regression (WR). The customization and the advantage of this approach over the existing methods are presented below:•The patterns in the data series of a hydrological variable and its related climatic factors are revealed by the wavelet analysis at different time scales.•The hydro-climate relationship of each pattern is revealed by the regression method based on the results of wavelet analysis.•The advantage of this approach over the existing methods is that the approach provides a routing to discover the hidden patterns in the stochastic and non-stationary data and quantitatively describe the hydro-climate relationships at different time scales.

Multiaxial Fatigue Spectrum Editing by Using Combined Wavelet Analysis and Stress Invariant Approach

The practicalities of structural fatigue testing limit the fidelity of the cyclic load history that can be applied to a test structure. Testing is, therefore, a compromise between fatigue damage fidelity and test economy. A new methodology is proposed for multiaxial loading spectrum editing to extract cycles that contribute negligible damage during fatigue crack initiation. The method is based on projection by projection (PbP) technique and wavelet transform analysis (WTA) procedure. In this approach, the cycles with negligible contribution to damage in every decoupled projected loading path (i.e. obtained from PbP approach) are extracted using the WTA procedure. Each extracted segment is then replaced with an equivalent cycle that produces the same amount of damage. The effectiveness of the edited spectrums is evaluated by the degree of fatigue damage retention as the original damage and preservation of statistical parameter values.As a case study, the proposed approach has been applied to the numerically produced random bending-torsion fatigue spectrum in plane-stress condition. The result shows an average of 75% reduction of the original spectrums with retention of 90% of the original spectrums’ damage values.

Inversion of particle size distributions based on wavelet analysis

ABSTRACTIn the Earth’s radiative budget, the role aerosols play in climate change depends on their particle size distribution. To address disadvantages linked to obtaining particle size distributions using traditional inversion algorithms, we propose a novel method combining wavelet analysis and Tikhonov regularization to solve the Fredholm integral equation of the first kind. This method can retrieve aerosol particle distributions, using aerosol optical thickness (AOT) from a CE-318 sun photometer. Experiments were carried out to verify the information retrieved using this new algorithm. AOT and particle size distributions were analysed and retrieved during various weather conditions, including dust storms, haze, fog, thunderstorms, and sunny skies. In addition, the seasonal average optical thickness and aerosol particle size distributions for the Yinchuan area in China were studied over a recent four-year period. Our results showed that particle size distributions were bimodal during dusty conditions, but unimodal during all other weather conditions studied. Moreover, our results indicate that air quality improved over two recent years.

Financial Time Series Prediction Based on Deep Learning

By combining wavelet analysis with Long Short-Term Memory (LSTM) neural network, this paper proposes a time series prediction model to capture the complex features such as non-linearity, non-stationary and sequence correlation of financial time series. The LSTM is then applied to the prediction of the daily closing price of the Shanghai Composite Index as well as the comparison of its prediction ability with machine learning models such as multi-layer perceptron, support vector machine and K-nearest neighbors. The empirical results show that the LSTM performs a better prediction effect, and it shows excellent effects on the static prediction and dynamic trend prediction of the financial time series, which indicates its applicability and effectiveness to the prediction of financial time series. At the same time, both wavelet decomposition and reconstruction of financial time series can improve the generalization ability of the LSTM prediction model and the prediction accuracy of long-term dynamic trend.

Analysis of electrocardiosignals for formation of the diagnostic features of post-traumatic myocardial dystrophy

The possibilities of high-resolution electrocardiography (HR ECG) application for diagnostics of post-traumatic myocardial dystrophy having multifactorial genesis is considered in this paper. Numerical processing and analysis of electrocardiograms that belong to patients from armed forces after explosive-driven injuries have been performed based on clinical studies. Complex method of cardiosignal analysis based on combination of wavelet analysis, eigenvector decomposition and principal component analysis is developed. This method revealed that low-amplitude deviations in ECG signal in case of post-traumatic myocardial dystrophy have low-frequency nature that is linked to slow electro-physiological processes. It is shown that these low-frequency, low-amplitude components appear at a high levels (8th and 9th) of decomposition in case of 9-level wavelet decomposition of averaged cardio cycles. Integral parameters for identification of post-traumatic myocardial dystrophy features are suggested and determined on the basis of principal component analysis. These parameters are squared sum of signal projections to eigenspaces H k and mean eigenvalues of covariance matrices of electrocardiosignals ensembles λmean.

Noise reduction for lidar returns using self-adaptive wavelet neural network

Lidar has been widely applied in many fields, such as meteorology and environment. However, because lidar returns are very weak, the influence of noise on useful signal is very serious. To obtain useful lidar return signals from raw data, a self-adaptive method combining wavelet analysis and a neural network that suppresses noise is proposed, in which the orthogonal Daubechies wavelet family serves as node functions in the hidden layer of the neural network, a search algorithm is selected to optimize the parameters and thresholds, and the Levenberg–Marquardt algorithm is adopted in the neural network gradient algorithm. Some comparative experiments were carried out to verify the feasibility of the noise reduction method and the results showed that the signal-to-noise ratio (SNR) of the common wavelet threshold denoising method is about 10, while that of the self-adaptive wavelet neural network denoising method is more than 20. From the experimental results, it can be seen that the wavelet neural network denoising method has less distortion and a higher SNR value than other methods, giving it superior performance.

Modeling activity patterns of wildlife using time-series analysis.

The study of wildlife activity patterns is an effective approach to understanding fundamental ecological and evolutionary processes. However, traditional statistical approaches used to conduct quantitative analysis have thus far had limited success in revealing underlying mechanisms driving activity patterns. Here, we combine wavelet analysis, a type of frequency‐based time‐series analysis, with high‐resolution activity data from accelerometers embedded in GPS collars to explore the effects of internal states (e.g., pregnancy) and external factors (e.g., seasonal dynamics of resources and weather) on activity patterns of the endangered giant panda (Ailuropoda melanoleuca). Giant pandas exhibited higher frequency cycles during the winter when resources (e.g., water and forage) were relatively poor, as well as during spring, which includes the giant panda's mating season. During the summer and autumn when resources were abundant, pandas exhibited a regular activity pattern with activity peaks every 24 hr. A pregnant individual showed distinct differences in her activity pattern from other giant pandas for several months following parturition. These results indicate that animals adjust activity cycles to adapt to seasonal variation of the resources and unique physiological periods. Wavelet coherency analysis also verified the synchronization of giant panda activity level with air temperature and solar radiation at the 24‐hr band. Our study also shows that wavelet analysis is an effective tool for analyzing high‐resolution activity pattern data and its relationship to internal and external states, an approach that has the potential to inform wildlife conservation and management across species.