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High-frequency (HF) signals are ubiquitous in the industrial world and are of great use for monitoring of industrial assets. Most deep-learning tools are designed for inputs of fixed and/or very limited size and many successful applications of deep learning to the industrial context use as inputs extracted features, which are a manually and often arduously obtained compact representation of the original signal. In this paper, we propose a fully unsupervised deep-learning framework that is able to extract a meaningful and sparse representation of raw HF signals. We embed in our architecture important properties of the fast discrete wavelet transform (FDWT) such as 1) the cascade algorithm; 2) the conjugate quadrature filter property that links together the wavelet, the scaling, and transposed filter functions; and 3) the coefficient denoising. Using deep learning, we make this architecture fully learnable: Both the wavelet bases and the wavelet coefficient denoising become learnable. To achieve this objective, we propose an activation function that performs a learnable hard thresholding of the wavelet coefficients. With our framework, the denoising FDWT becomes a fully learnable unsupervised tool that does not require any type of pre- or postprocessing or any prior knowledge on wavelet transform. We demonstrate the benefits of embedding all these properties on three machine-learning tasks performed on open-source sound datasets. We perform an ablation study of the impact of each property on the performance of the architecture, achieve results well above baseline, and outperform other state-of-the-art methods.

Prediction of Remaining Useful Life (RUL) of lithium-ion batteries plays a significant role in battery health management. Battery capacity is often chosen as the Health Indicator (HI) in research on lithium-ion battery RUL prediction. In the rest time of batteries, capacity will produce a certain degree of regeneration phenomenon, which exists in the use of each battery. Therefore, considering the capacity regeneration phenomenon in RUL prediction of lithium-ion batteries is helpful to improve the prediction performance of the model. In this paper, a novel method fusing the wavelet decomposition technology (WDT) and the Nonlinear Auto Regressive neural network (NARNN) model for predicting the RUL of a lithium-ion battery is proposed. Firstly, the multi-scale WDT is used to separate the global degradation and local regeneration of a battery capacity series. Then, the RUL prediction framework based on the NARNN model is constructed for the extracted global degradation and local regeneration. Finally, the two parts of the prediction results are combined to obtain the final RUL prediction result. Experiments show that the proposed method can not only effectively capture the capacity regeneration phenomenon, but also has high prediction accuracy and is less affected by different prediction starting points.

The use of digital technologies for processing and diagnosing electrocardiogram signals using wavelet-analysis can significantly improve the efficiency and quality of parameter estimations of the pacemaker configuration during implantation. It is also efficient in the process of correction of functional modes of cardiac pacemaker and diagnostics to eliminate postoperative complications, etc. A special processing of complex cardio signals at a qualitatively new level is an indispensable condition for the decisive improvement of the processing of current values of diagnosed parameters, widespread use of digital instruments for sound and informed decision-making on the provision of medical care and the treatment of people with diseases of the cardiovascular system. The article discusses the approximation method. Digital technologies are implemented using MATLAB computing environment.

Detecting motor imagery from electrocardiographic (ECG) signals is complex but crucial in developing advanced neuroprosthetic devices and brain-computer interface (BCI) systems. In most cases, linear models applied using conventional methods are not appropriate for the time-varying and non-linear nature represented by the ECG characteristics, resulting in weak performances. This research addresses this problem, combining Wavelet Packet Decomposition and Multi-Scale Convolutional Neural Networks to improve the feature extraction mechanism and classification accuracy. ECG data is pre-processed from the PhysioNet EEG Motor Movement/Imagery Dataset to remove noise and standardize signals. WPD is thus applied to decompose the signals into detailed frequency components to be input as features in the proposed Multi-Scale CNN. Different kernel sizes are implemented in these parallel convolutional layers to learn complicated features at various hierarchical resolutions. The proposed architecture is evaluated using performance parameters such as accuracy 92%, precision 89%, recall 93%, F1 score 91%, and ROCAUC 95%. These results showed that the model outperformed the earlier-used traditional methods, such as Support Vector Machines (SVM) and Random Forests, better-detecting motor imagery. This research emphasizes the integrative power of advanced signal processing techniques with deep learning in analyzing biomedical signals, providing a powerful solution to advancing neuroprosthetic and BCI technologies.

Wind power generation is one of the renewable energy generation methods which maintains good momentum of development at present. However, its extremely intense intermittences and uncertainties bring great challenges to wind power integration and the stable operation of wind power grids. To achieve accurate prediction of wind power generation in China, a hybrid prediction model based on the combination of Wavelet Decomposition (WD) and Long Short-Term Memory neural network (LSTM) is constructed. Firstly, the nonstationary time series is decomposed into multidimensional components by WD, which can effectively reduce the volatility of the original time series and make them more stable and predictable. Then, the components of the original time series after WD are used as input variables of LSTM to predict the national wind power generation. Forty points were used, 80% as training samples and 20% as testing samples. The experimental results show that the MAPE of WD-LSTM is 5.831, performing better than other models in predicting wind power generation in China. In addition, the WD-LSTM model was used to predict the wind power generation in China under different development trends in the next two years.

In this research, monthly wind speed time series of the Kirsehir was investigated using the stand-alone, hybrid and ensemble models. The artificial neural networks, Gaussian process regression, support vector machines and multivariate adaptive regression splines were employed as stand-alone machine learning models, while the discrete wavelet transform was utilized as a pre-processing technique to create hybrid models. Moreover, for the first time in wind speed predictions, we generated a multi-stage ensemble model by using the M5 Model Tree (M5) algorithm to increase the model accuracies. Two major tasks considered to be necessary, in which the first is to obtain the lag times by using autocorrelation functions, and the latter is to determine the optimum mother wavelet as well as the decomposition level to reduce the uncertainties in wavelet modeling. The results revealed that the hybrid wavelet models outperformed the stand-alone models, while a significant improvement was also observed in M5 ensemble models as the highest Nash–Sutcliffe efficiency coefficient values were obtained in M5 hybrid wavelet multi-stage ensemble models for each lead time prediction. The findings of the study were assessed with respect to the various performance indicators and Kruskal–Wallis test to indicate whether the results are statically significant. The proposed multi-stage ensemble framework also benchmarked with the classical tree-based ensembles, such as Random forest, AdaBoost and XGBoost.

Driving while fatigued is just as dangerous as drunk driving and may result in car accidents. Heart rate variability (HRV) analysis has been studied recently for the detection of driver drowsiness. However, the detection reliability has been lower than anticipated, because the HRV signals of drivers were always regarded as stationary signals. The wavelet transform method is a method for analyzing non-stationary signals. The aim of this study is to classify alert and drowsy driving events using the wavelet transform of HRV signals over short time periods and to compare the classification performance of this method with the conventional method that uses fast Fourier transform (FFT)-based features. Based on the standard shortest duration for FFT-based short-term HRV evaluation, the wavelet decomposition is performed on 2-min HRV samples, as well as 1-min and 3-min samples for reference purposes. A receiver operation curve (ROC) analysis and a support vector machine (SVM) classifier are used for feature selection and classification, respectively. The ROC analysis results show that the wavelet-based method performs better than the FFT-based method regardless of the duration of the HRV sample that is used. Finally, based on the real-time requirements for driver drowsiness detection, the SVM classifier is trained using eighty FFT and wavelet-based features that are extracted from 1-min HRV signals from four subjects. The averaged leave-one-out (LOO) classification performance using wavelet-based feature is 95% accuracy, 95% sensitivity, and 95% specificity. This is better than the FFT-based results that have 68.8% accuracy, 62.5% sensitivity, and 75% specificity. In addition, the proposed hardware platform is inexpensive and easy-to-use.

Edge detection of the sources of potential field anomaly is an important step in the interpretation of subsurface source geometries. The conventional methods based on calculation of horizontal or vertical derivatives identify the edges or center of sources by minima, maxima, or zero values in the transformed data. We present a wavelet source edge detector method (WSED) using wavelet multiresolution analysis to identify potential field sources boundaries. The two-dimensional wavelet decomposition is an effective method to understand the frequency components of the signal in different directions. We use a 2D-discrete wavelet transform using Haar wavelets in resolving lateral edges for source edge detection. We test the method on synthetic magnetic anomalies due to sources of complex geometries generated using prismatic sources. We investigated the robustness of the method on the magnetic data of the Bishop model and found the results useful in resolving the edges. We applied the method to gravity data of the north Delhi fold belt, India, to identify boundaries of different geological formations. Our results indicate distinct properties of the source edges in the wavelet domain, which is for the first time reported for the interpretation of the potential field anomalies.

The paper proposes an anomaly detection method for UAVs based on wavelet decomposition and stacked denoising autoencoder. This method takes the negative impact of noisy data and the feature extraction capabilities of deep learning models into account. It aims to improve the accuracy of the proposed anomaly detection method with wavelet decomposition and stacked denoising autoencoder methods. Anomaly detection based on UAV flight data is an important method of UAV condition monitoring and potential abnormal state mining, which is an important means to reduce the risk of UAV flight accidents. However, the diversity of UAV mission scenarios leads to a complex and harsh environment, so the acquired data are affected by noise, which brings challenges to accurate anomaly detection based on UAV data. Firstly, we use wavelet decomposition to denoise the original data; then, we used the stacked denoising autoencoder to achieve feature extraction. Finally, the softmax classifier is used to realize the anomaly detection of UAV. The experimental results demonstrate that the proposed method still has good performance in the case of noisy data. Specifically, the Accuracy reaches 97.53%, the Precision is 97.50%, the Recall is 91.81%, and the F1-score is 94.57%. Furthermore, the proposed method outperforms the four comparison models with more outstanding performance. Therefore, it has significant potential in reducing UAV flight accidents and enhancing operational safety.

Solar photovoltaic (PV) power forecasting has become an important issue with regard to the power grid in terms of the effective integration of large-scale PV plants. As the main influence factor of PV power generation, solar irradiance and its accurate forecasting are the prerequisite for solar PV power forecasting. However, previous forecasting approaches using manual feature extraction (MFE), traditional modeling and single deep learning (DL) models could not satisfy the performance requirements in partial scenarios with complex fluctuations. Therefore, an improved DL model based on wavelet decomposition (WD), the Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM) is proposed for day-ahead solar irradiance forecasting. Given the high dependency of solar irradiance on weather status, the proposed model is individually established under four general weather type (i.e., sunny, cloudy, rainy and heavy rainy). For certain weather types, the raw solar irradiance sequence is decomposed into several subsequences via discrete wavelet transformation. Then each subsequence is fed into the CNN based local feature extractor to automatically learn the abstract feature representation from the raw subsequence data. Since the extracted features of each subsequence are also time series data, they are individually transported to LSTM to construct the subsequence forecasting model. In the end, the final solar irradiance forecasting results under certain weather types are obtained via the wavelet reconstruction of these forecasted subsequences. This case study further verifies the enhanced forecasting accuracy of our proposed method via a comparison with traditional and single DL models.