Combined Wavelet Transform Research Articles

Biomedical ECG Signal Compression by Combining Wavelet Transform and Unsupervised Autoencoder Techniques

Abstract: Storing biomedical signal data is a significant concern in the field of biomedical signal processing because it requires a substantial amount of storage space. These biomedical signals often contain hours of information, necessitating extensive storage capacity. Researchers employ Electrocardiogram (ECG) signal compression techniques to address this issue. However, compressing the ECG signal could potentially lead to the loss of important features or data. This loss may adversely impact the accurate analysis of heart patient conditions. This paper introduces a novel approach for compressing ECG signals by the combined power of Wavelet Transform (WT) and unsupervised Autoencoder (AE) techniques. ECG signal compression plays a crucial role in reducing data storage and transmission requirements without compromising diagnostic accuracy. The proposed methodology, termed WT-AutoEncoder, integrates Wavelet Transform for signal decomposition and feature extraction, followed by an Autoencoder for efficient encoding and reconstruction of the original signal. Unlike conventional methods, this approach utilizes the strengths of both WT and AE to achieve high compression ratios while preserving signal accuracy. The study conducts comprehensive experiments and evaluations using benchmark MIT-BIH datasets to assess the performance of the WT-AutoEncoder on specific records (101-109) in terms of compression ratio of 32.31, PRDN of 33.26, PRD of 3.06, and QS of 13.49. The final results demonstrate the effectiveness of the proposed model compared with existing methods in compressing ECG signals while maintaining high accuracy, suggesting its potential for secure transmission and storage in various healthcare applications.

Hybrid model combining LSTM with discrete wavelet transformation to predict surface methane concentration in the Arctic Island Belyy

In this paper, we propose a hybrid model that combines wavelet transformation of the raw data and an artificial neural network with long short-term memory (LSTM). This model allows researchers to increase the accuracy of time series forecasting.The model is based on data from environmental monitoring of greenhouse gases on the Belyy Island of the Yamal-Nenets Autonomous Okrug, Russia.The raw data for building the proposed model were obtained in July–August 2016. The CH4 concentration time series was decomposed using a discrete wavelet transform into four components - one approximating and three detailing. These components, along with a timed temperature series, were used to train six ANNs—two exogenous input autoregressive networks (NAR) and four LSTM networks. The forecast was calculated as the sum of forecasts for each of the components. Forecast accuracy was assessed using several indices (mean absolute error (MAE), root mean square error (RMSE), mean square relative error (RMSRE), Willmott's agreement index (IA1, IA2)) and a Taylor diagram. The hybrid model based on LSTM showed the best accuracy. The hybrid model based on LSTM showed the best accuracy. MAE, RMSE, and RMSRE errors decreased by more than 70%. In terms of IA1 and IA2, the models improved by 11% and 30% (when comparing the best hybrid models LSTM and NAR. For the hybrid LSTM model errors RMSE, RMSRE, and MAE are more than 20% less than for the base LSTM model for training in which data without wavelet transform were used. Willmott agreement indices (IA1, IA2) rose from 32% to 59%, depending on the models being compared. So, the increase in accuracy after applying the described approach was up to 79% for models based on LSTM (more precisely, from 20% to 79%, depending on the indicator). Applying wavelet transform data to train the NAR-based model reduced MAE, RMSE, and RMSRE errors by 27%, 30%, and 31%, respectively. The Willmott agreement indices (IA1, IA2) rose from 41% to 45% respectively. The Taylor diagram also shows the advantage of the proposed approach.

Модель для прогнозирования поверхностной концентрации метана в арк­тическом регионе, основанная на искусственной нейронной сети с длинной цепью элементов краткосрочной памяти и вейвлет-преобразованием исходных данных

The study of the dynamics of greenhouse gases in the Arctic regions of the planet is becoming increasingly important. Such studies are especially relevant due to the climate change observed in this region. The paper propose a hybrid model that combines wavelet transformation of the original data and an artificial neural network with a long chain of short-term memory (LSTM) elements to predict changes in the surface methane concentration in the Arctic latitudes. The methane concentration time series via a discrete wavelet transform was decomposed into four components — one approximating and three detailing ones. These components were used to train the LSTM network. The forecast was calculated as the sum of forecasts for each of the components. Three predictive models were built. In the first, the LSTM network was trained in a non-linear autoregressive mode. The second one was a combination of discrete wavelet transform with LSTM neural network. An additional model based on a non-linear autoregressive neural network (NAR) was also used for comparison. The work is based on data from environmental monitoring of greenhouse gases on Bely Island, Yamalo-Nenets Autonomous Area of Russia. The initial data for building the proposed model were obtained within July-August 2017. The accuracy of the forecast was assessed using several indicators. The hybrid model based on LSTM showed the best accuracy.

Daily suspended sediment concentration forecast in the upper reach of Yellow River using a comprehensive integrated deep learning model

The precise prediction of suspended sediment concentration (SSC) is of great importance for river reservoir construction planning, water resource management, and ecological environment restoration. This research aims to improve SSC prediction accuracy by constructing a comprehensive and integrated deep learning model Wavelet-MGGP-CNN-LSTM (ICNN-LSTM), combining wavelet transformation (WT), multi-gene genetic programming (MGGP), convolutional neural network (CNN), and long short-term memory (LSTM) simultaneously. In ICNN-LSTM, the WT decomposes the signal and extracts time and frequency domain information, while the MGGP filters out redundant information. Then, the CNN and LSTM are integrated in a parallel and loosely coupled manner to form an initial combined model CNN-LSTM (CNN combined with LSTM) to process filtered information by WT and MGGP. Furthermore, this study compares the performance of ICNN-LSTM with CNN, LSTM, CNN-LSTM, ICNN (CNN embedded with WT and MGGP), ILSTM (LSTM embedded with WT and MGGP), artificial neural network (ANN), and the traditional sediment rating curve (SRC). The evaluation of prediction accuracy for all models was conducted using root mean square error (RMSE), Nash-Sutcliffe coefficient (NSC), coefficient of determination (R2), and mean absolute error (MAE) as performance indicators. The daily discharge and suspended sediment concentration series data from Tangnaihai Hydrological Station in the upper reaches of the Yellow River spanning from 1977 to 1987 were selected to train and test the models. Results show that, first, deep learning networks such as CNN and LSTM outperform the shallow neural network ANN, with LSTM providing higher accuracy than CNN. Second, the CNN-LSTM hybrid outperforms both CNN and LSTM models, exhibiting a nearly 89% improvement in NSC value compared to SRC in the test phase. Third, deep learning models such as ICNN, ILSTM, and ICNN-LSTM show significantly higher NSC values than CNN, LSTM, and CNN-LSTM models in the test phase, with improvements of 13.8%, 5.7%, and 12.1%, respectively. Moreover, compared to SRC, the proposed ICNN-LSTM model improves NSC value by nearly 140% in the test phase. The proposed ICNN-LSTM model, integrating the advantages of WT, deep learning, and ensemble learning, provides accurate and reliable predictions and serves as a reference for time series prediction modeling.

Prediction of Air Quality Combining Wavelet Transform, DCCA Correlation Analysis and LSTM Model

In the context of global climate change, air quality prediction work has a substantial impact on humans’ daily lives. The current extensive usage of machine learning models for air quality forecasting has resulted in significant improvements to the sector. The long short-term memory network is a deep learning prediction model, which adds a forgetting layer to a recurrent neural network and has several applications in air quality prediction. The experimental data presented in this research include air pollution data (SO2, NO2, PM10, PM2.5, O3, and CO) and meteorological data (temperature, barometric pressure, humidity, and wind speed). Initially, using air pollution data to calculate the air pollution index (AQI) and the wavelet transform with the adaptive Stein risk estimation threshold is utilized to enhance the quality of meteorological data. Using detrended cross-correlation analysis (DCCA), the mutual association between pollution elements and meteorological elements is then quantified. On short, medium, and long scales, the prediction model’s accuracy increases by 1%, 1.6%, 2%, and 5% for window sizes (h) of 24, 48, 168, and 5000, and the efficiency increases by 5.72%, 8.64%, 8.29%, and 3.42%, respectively. The model developed in this paper has a substantial improvement effect, and its application to the forecast of air quality is of immense practical significance.

Deep Transfer Learning-Based Fault Diagnosis Using Wavelet Transform for Limited Data

Although various deep learning techniques have been proposed to diagnose industrial faults, it is still challenging to obtain sufficient training samples to build the fault diagnosis model in practice. This paper presents a framework that combines wavelet transformation and transfer learning (TL) for fault diagnosis with limited target samples. The wavelet transform converts a time-series sample to a time-frequency representative image based on the extracted hidden time and frequency features of various faults. On the other hand, the TL technique leverages the existing neural networks, called GoogLeNet, which were trained using a sufficient source data set for different target tasks. Since the data distributions between the source and the target domains are considerably different in industrial practice, we partially retrain the pre-trained model of the source domain using intermediate samples that are conceptually related to the target domain. We use a reciprocating pump model to generate various combinations of faults with different severity levels and evaluate the effectiveness of the proposed method. The results show that the proposed method provides higher diagnostic accuracy than the support vector machine and the convolutional neural network under wide variations in the training data size and the fault severity. In particular, we show that the severity level of the fault condition heavily affects the diagnostic performance.

Combined Wavelet Transform With Long Short-Term Memory Neural Network for Water Table Depth Prediction in Baoding City, North China Plain

Accurate estimation of water table depth dynamics is essential for water resource management, especially in areas where groundwater is overexploited. In recent years, as a data-driven model, artificial neural networks (NNs) have been widely used in hydrological modeling. However, due to the non-stationarity of water table depth data, the performance of NNs in areas of over-exploitation is challenging. Therefore, reducing data noise is an essential step before simulating the water table depth. This research proposed a novel method to model the non-stationary time series data of water table depth through combing the advantages of wavelet analysis and Long Short-Term Memory (LSTM) neural network (NN). A typical groundwater over-exploitation area, Baoding, North China Plain (NCP), was selected as a study area. To reflect the impact of anthropogenic activities, the variables harnessed to develop the model includes temperature, precipitation, evaporation, and some socio-economic data. The results show that decomposing the time series of the water table depth into three sub-temporal components by Meyer wavelets can significantly improve the simulation effect of LSTM on the water table depth. The average NSE (Nash-Sutcliffe efficiency coefficient) value of all the sites increased from 0.432 to 0.819. Additionally, a feedforward neural network (FNN) is used to compare forecasts over 12-months. As expected, wavelet-LSTM outperforms wavelet-FNN. As the prediction time increases, the advantages of wavelet-LSTM become more evident. The wavelet-LSTM is satisfactory for forecasting the water table depth at most in 6 months. Furthermore, the importance of input variables of wavelet-LSTM is analysed by the weights of the model. The results indicate that anthropogenic activities influence the water table depth significantly, especially in the sites close to the Baiyangdian Lake, the largest lake in the North China Plain. This study demonstrates that the wavelet-LSTM model provides an option for water table depth simulation and predicting areas of over-exploitation of groundwater.

Comparative Study of Short-Term Forecasting Methods for Soybean Oil Futures Based on LSTM, SVR, ES and Wavelet Transformation

Short-term forecasting of futures market is valuable and is also a technical challenge. In this paper, a hybrid approach for soybean oil futures price forecasting is proposed based on time-series analysis methods. The method combines wavelet transformation and exponential smoothing so that the characteristics of the time series can be captured at different time scales, and forecasting based on exponential smoothing is applied at each time scale. A comparative case study is then conducted that compares the proposed method with other three methods which are an RNN network with Long Short-Term Memory units, a Support-Vector Regression model, and an Exponential Smoothing model without wavelet decomposition to the time series. It could be concluded that the forecasting error performance of ES and Wavelet-ES was better than LSTM and SVR, and the Wavelet-ES achieved the best results for the direction forecasting. The case study provides valuable reference for application of short-term futures price forecasting.

A Study on Fault Diagnosis of Rotating Machinery Combined Wavelet Transform with VMD

Effective diagnosis of rotating machinery is difficult in view of the complex structure, weak early fault signals, non-stationary and non-linear vibration signals, and low signal-to-noise ratio. In this paper, a fault diagnosis method is proposed based on particle swarm optimization (PSO) and variational modal decomposition (VMD). Firstly, wavelet packet threshold is denoised on the signal, VMD is decomposed on the reconstructed signal, and PSO is optimized on the inherent mode function (IMF) obtained from decomposition so as to determine the best IMF function. Then Hilbert transform and envelope spectrum analysis are carried out on the IMF function, and the envelope spectrum analysis result is compared with theoretical calculation frequency to finally determine the fault type. The results indicate that this method can effectively reduce noise components in signals, extract weak fault information and realize fault diagnosis.

A Combined Wavelet Transform and Recurrent Neural Networks Scheme for Identification of Hydrocarbon Reservoir Systems From Well Testing Signals

AbstractOil and gas are likely the most important sources for producing heat and energy in both domestic and industrial applications. Hydrocarbon reservoirs that contain these fuels are required to be characterized to exploit the maximum amount of their fluids. Well testing analysis is a valuable tool for the characterization of hydrocarbon reservoirs. Handling and analysis of long-term and noise-contaminated well testing signals using the traditional methods is a challenging task. Therefore, in this study, a novel paradigm that combines wavelet transform (WT) and recurrent neural networks (RNN) is proposed for analyzing the long-term well testing signals. The WT not only reduces the dimension of the pressure derivative (PD) signals during feature extraction but it efficiently removes noisy data. The RNN identifies reservoir type and its boundary condition from the extracted features by WT. Results confirmed that the five-level decomposition of the PD signals by the Bior 1.1 filter provides the best features for classification. A two-layer RNN model with nine hidden neurons correctly detects 3202 out of 3298 hydrocarbon reservoir systems. Performance of the proposed approach is checked using smooth, noisy, and real field well testing signals. Moreover, a comparison is done among predictive accuracy of WT-RNN, traditional RNN, conventional multilayer perceptron (MLP) neural networks, and couple WT-MLP approaches. The results confirm that the coupled WT-RNN paradigm is superior to the other considered smart machines.

Time series analysis for multi-dimensional dynamical systems combining wavelet transformation and local principal component analysis

Abstract To analyze trajectories for systems of many degrees of freedom, we propose a new method called wavelet local principal component analysis (WlPCA) combining the wavelet transformation and local PCA in time. Our method enables us to reduce the dimensionality of time series both in degrees of freedom and frequency so that characteristic features of oscillatory behavior can be captured. To test the new method, we apply WlPCA to a non-autonomous model of multiple degrees of freedom, the Froeschlé maps of $N=2$ and $N=4$, which correspond to autonomous systems of three and five degrees of freedom, respectively. The eigenvalues and eigenvectors obtained by WlPCA reveal those times when frequency variation exhibits switching between relatively stationary features. Moreover, further analyses indicate which degrees of freedom and frequencies are involved in the switching. We confirm that the switching corresponds to the onset of transport in phase space. These findings imply that, even for systems of larger degrees of freedom, barriers can exist in phase space that block transport for a finite time, thereby dividing the phase space into multiple quasi-stationary regions. Thus, our method is promising for understanding dynamics in systems of many degrees of freedom, such as vibrational-energy redistribution in molecules.

Unsupervised color texture segmentation based on multi-scale region-level Markov random field models

In the field of color texture segmentation, region-level Markov random field model (RMRF) has become a focal problem because of its efficiency in modeling the large-range spatial constraints. However, the RMRF defined on a single scale cannot describe the un-stationary essence of the image, which highly limits its robustness. Hence, by combining wavelet transformation and the RMRF model, we present a multi-scale RMRF (MsRMRF) model in wavelet domainin this paper. In the Bayesian framework, the proposed model seamlessly integrates the multi-scale information stemmed from both the original image and the region-level spatial constraints. Therefore, the new model can accurately describe the characteristics of different kinds of texture. Based on MsRMRF, an unsupervised segmentation algorithm is designed for segmenting color texture images. Both synthetic color texture images and remote sensing images are employed in the comparative experiments, and the experimental results show that the proposed method can obtain more accurate segmentation results than the competitors.

Application of Wavelet Neuro-Fuzzy System (WNFS) method for stock forecasting

Forecasting is a very important element in decision making, because the effectiveness of a decision, generally depends on several factors that we cannot see when the decision was taken. In this study, the Wavelet Neuro-Fuzzy System (WNFS) model that combines wavelet transformation and neuro-fuzzy techniques is applied to forecast daily closing stock price data of BMRI.JK. The observed daily stock price data are decomposed into some sub-series components by maximal overlap discrete wavelet transform (MODWT), then the appropriate sub-series that have higher correlation to the real data are used as inputs of the neuro-fuzzy model for daily forecasting stock price for three days in advance. The neuro-fuzzy model is begun with determining the membership value of each data using Fuzzy C-Means, followed by fuzzy inference procedure of the Sugeno model. The result shows that the presence of wavelet input in Neuro-Fuzzy System, can provide optimal prediction in daily stock price data, with small error value of predicted result. This would be helped investors or economists to produce meaningful information in either buy or sell a stock.

An Application Study of DNA Structural Properties for Promoter Prediction with Wavelet and Support Vector Machine

Conventional promoter predictions are mainly based on the sequential compositional features of the promoter sequences, referred to as motifs (for example, the TATA-box). The wide diversity and ambiguity of motifs limit the performance of conventional predictions methods. However, recent research has revealed a strong correlation between promoters and their second-order structural information. We have studied a promoter prediction method that combines wavelet transformation with a support vector machine (SVM). This method converts positive and negative sets of DNA sequences to numerical sequences based on some feature of the DNA, and then transforms the numerical sequences into wavelet data. The positive and negative sequence sets provide the training data for the SVM. Finally, the trained SVM is used for promoter prediction. Our previous studies adopted a simple coding scheme based on the difference between the C-G and T-A pairs of the DNA sequence. This paper replaces the simple coding scheme with the second-order structural information of DNA, and evaluates the performance and possibility of our promoter prediction scheme.

Using Wavelet Transformation and Edge Detection to Generate a Depth Map from a Single Image

A depth map is essential for 3D display. Traditional depth maps are derived from multi-images. Producing a depth map from a single image is a more challenging problem and much more difficult than that of from multi-images. We propose a novel approach that combines wavelet transformation with edge detection to generate depth information from a single image. A depth map is then generated by depth prediction. Peak signal-to-noise ratio (PSNR), the structural similarity image measure (SSIM), and computation time are used to evaluate the performance of the proposed algorithm. The experimental results reveal that the PSNR and SSIM of the proposed algorithm are larger than those produced in the traditional approach. The computation time of the proposed algorithm is less than that produced by the traditional approach. Furthermore, 1000 test images and the crossponding depth maps are produced in this study. The average of the three metrics was found to be superior to those of the traditional approach. The statistic tests were also significant for PSNR and TIME between the two approaches. We have also written and files four patent applications with respect to this work.

BEAT CLASSIFICATION USING HYBRID WAVELET TRANSFORM BASED FEATURES AND SUPERVISED LEARNING APPROACH

This paper describes an automatic heartbeat recognition based on QRS detection, feature extraction and classification. In this paper five different type of ECG beats of MIT BIH arrhythmia database are automatically classified. The proposed method involves QRS complex detection based on the differences and approximation derivation, inversion and threshold method. The computation of combined Discrete Wavelet Transform (DWT) and Dual Tree Complex Wavelet Transform (DTCWT) of hybrid features coefficients are obtained from the QRS segmented beat from ECG signal which are then used as a feature vector. Then the feature vectors are given to Extreme Learning Machine (ELM) and k- Nearest Neighbor (kNN) classifier for automatic classification of heartbeat. The performance of the proposed system is measured by sensitivity, specificity and accuracy measures.

Wavelet regression and wavelet neural network models for forecasting monthly streamflow

This paper investigates the performance of wavelet-based regression models for monthly streamflow forecasting. The wavelet-based regression model combines wavelet transformation and multiple linear regression (LR). The wavelet-based regression forecasts are also compared to the wavelet-based neural network, which combines the wavelet transformation and feed forward neural network. The wavelet transformation has significantly positive effects on the modeling performance. In this study, the different approaches of the wavelet-based models were applied to forecast the monthly flow. The results show that the wavelet-based feed forward neural network and the wavelet-based linear regression (WLR) produce very good results for 1-month-ahead streamflow forecasting. Both techniques demonstrated an almost similar performance. Also, the result of the WLR5 model is better than the results of the other WLR models in terms of performance criteria.

Comparison of wavelet based hybrid models for daily evapotranspiration estimation using meteorological data

This paper investigates the comparative performance of wavelet based radial basis networks and multi linear regression in daily reference evapotranspiration estimation. The meteorological data (air temperature, solar radiation, wind speed, relative humidity) from two stations in the United States was evaluated for estimating models. The wavelet based radial basis network combines wavelet transformation and radial basis neural network, while the wavelet based regression model combines wavelet transformation and multi linear regression. The results show that the wavelet transformation has significantly positive effects on modeling performance. The wavelet based radial basis network provided the best performance evaluation criteria.

Fetal Electrocardiogram Extraction Based on SWT-MM Method

Fetal electrocardiogram (FECG) is of great importance due to the potentially precise information that FECG carries could assist clinicians in making more appropriate and timely decisions during pregnancy and labor. In this paper, a method based on combined Stationary Wavelet Transform and Modulus-Maxima (SWT-MM) method is proposed for extracting the complete morphology of the FECG from maternal abdominal ECG (AECG). It particularly provides a different way of constructing the maternal ECG (MECG) template. The Efficacy of the method was validated using real data in Non-Invasive Fetal Electrocardiogram Database. The morphology of the extracted FECG was clearly seen that the fetal R-peak detection by simple differential-threshold method acquired the average accuracy of 96.8%. The method provides additional important benefits of fast speed and automated control for applying into the fetal monitors. Therefore, the method is potentially a strong tool for FECG extraction, especially in real-time use.

Research on Combined Prediction Model for Busy Telephone Traffic

In order to improve the prediction accuracy of busy telephone traffic, this study proposes a busy telephone traffic prediction method that combines wavelet transformation and least square support vector machine (lssvm) model which is optimized by particle swarm optimization (pso) algorithm. Firstly, decompose the pretreatment of busy telephone traffic data with mallat algorithm and get low frequency component and high frequency component. Secondly, reconfigure each component and use pso_lssvm model predict each reconfigured one. Then the busy telephone traffic can be achieved. The experimental results show that the prediction model has higher prediction accuracy and stability.