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A new approach for enhancing the reliability and practicality of online tool condition monitoring (TCM) is introduced in the current research. This new method is based on analyzing raw force signals and processing cutting tool images. A new vision system based on a CCD camera is used to monitor the tool condition by collecting images of the rotating cutting tool during the milling operation, making it a convenient and feasible process. Firstly, image processing wear extraction based on the projection of the rotating tool is investigated in this study. This method demonstrated a high correlation with the experimental flank wear, reaching 99.37%. Then, the tool wear prediction method was developed by combining a hybrid deep learning algorithm with a raw signal multiresolution analysis method based on the wavelet transform to improve the accuracy of identifying tool wear. This method involves combining a hybrid deep learning algorithm that consists of a Convolutional Neural Network (CNN) and Bidirectional Long-Short Term Memory (BiLSTM) with Maximal Overlap Discrete Wavelet Transform (MODWT) for preprocessing signals. Cutting experiments using different tool sizes and parameters were performed on the vertical CNC milling machine. Finally, to evaluate the performance of the proposed model, its identification accuracy was compared to that of other deep learning and machine learning models. According to the experimental result and in contrast to available TCM methods, the proposed method improves the accuracy of tool wear condition recognition. The proposed model demonstrated the highest regression coefficient R compared with common prediction methods, equal to 99.5% on average.

In this paper, new features relevant to blood pressure (BP) estimation using photoplethysmography (PPG) are presented. A total of 195 features, including the proposed ones and those already known in the literature, have been calculated on a set composed of 50,000 pulses from 1080 different patients. Three feature selection methods, namely Correlation-based Feature Selection (CFS), RReliefF and Minimum Redundancy Maximum Relevance (MRMR), have then been applied to identify the most significant features for BP estimation. Some of these features have been extracted through a novel PPG signal enhancement method based on the use of the Maximal Overlap Discrete Wavelet Transform (MODWT). As a matter of fact, the enhanced signal leads to a reliable identification of the characteristic points of the PPG signal (e.g., systolic, diastolic and dicrotic notch points) by simple means, obtaining results comparable with those from purposely defined algorithms. For systolic points, mean and std of errors computed as the difference between the locations obtained using a purposely defined already known algorithm and those using the MODWT enhancement are, respectively, 0.0097 s and 0.0202 s; for diastolic points they are, respectively, 0.0441 s and 0.0486 s; for dicrotic notch points they are 0.0458 s and 0.0896 s. Hence, this study leads to the selection of several new features from the MODWT enhanced signal on every single pulse extracted from PPG signals, in addition to features already known in the literature. These features can be employed to train machine learning (ML) models useful for estimating systolic blood pressure (SBP) and diastolic blood pressure (DBP) in a non-invasive way, which is suitable for telemedicine health-care monitoring.

Wavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the implications of using the maximal overlap discrete wavelet transform (MODWT) versus the well-known discrete wavelet transform (DWT). We demonstrate that the spectroscopic features extracted using DWT can vary over different overlapping frequency ranges. On the contrary, MODWT is translation-invariant and results in identical features, regardless of the spectral range used for its implementation.We also demonstrate that the details coefficients obtained by the multiresolution analysis (MRA) using MODWT are associated with zero-phase filters. In contrast, DWT details coefficients suffer from misalignments originated from the down- and upsampling operations in DWT pyramid algorithm. Such misalignments have adverse effects when it is critical to retain the exact location of the absorption lines. We study the differences of DWT and MODWT both analytically and experimentally, using reflection THz-TDS measurements of α-lactose monohydrate. This manuscript can guide the researchers to select the right wavelet analysis tool for their specific application of the THz spectroscopy.

The use of electrical conductivity (EC) as a water quality indicator is useful for estimating the mineralization and salinity of water. The objectives of this study were to explore, for the first time, extreme learning machine (ELM) and wavelet-extreme learning machine hybrid (WA-ELM) models to forecast multi-step-ahead EC and to employ an integrated method to combine the advantages of WA-ELM models, which utilized the boosting ensemble method. For comparative purposes, an adaptive neuro-fuzzy inference system (ANFIS) model, and a WA-ANFIS model, were also developed. The study area was the Aji-Chay River at the Akhula hydrometric station in Northwestern Iran. A total of 315 monthly EC (µS/cm) datasets (1984–2011) were used, in which the first 284 datasets (90% of total datasets) were considered for training and the remaining 31 (10% of total datasets) were used for model testing. Autocorrelation function (ACF) and partial autocorrelation function (PACF) demonstrated that the 6-month lags were potential input time lags. The results illustrated that the single ELM and ANFIS models were unable to forecast the multi-step-ahead EC in terms of root mean square error (RMSE), coefficient of determination (R2) and Nash–Sutcliffe model efficiency coefficient (NSC). To develop the hybrid WA-ELM and WA-ANFIS models, the original time series of lags as inputs, and time series of 1, 2 and 3 month-step-ahead EC values as outputs, were decomposed into several sub-time series using different maximal overlap discrete wavelet transform (MODWT) functions, namely Daubechies, Symlet, Haar and Coiflet of different orders at level three. These sub-time series were then used in the ELM and ANFIS models as an input dataset to forecast the multi-step-ahead EC. The results indicated that single WA-ELM and WA-ANFIS models performed better than any ELM and ANFIS models. Also, WA-ELM models outperformed WA-ANFIS models. To develop the boosting multi-WA-ELM and multi-WA-ANFIS ensemble models, a least squares boosting (LSBoost) algorithm was used. The results showed that boosting multi-WA-ELM and multi-WA-ANFIS ensemble models outperformed the individual WA-ELM and WA-ANFIS models.

This research is the earliest attempt to understand the impact of inflation and the interest rate on output growth in the context of Pakistan using the wavelet transformation approach. For this study, we used monthly data on inflation, the interest rate, and industrial production from January 1991 to May 2020. The COVID-19 pandemic has affected economies around the world, especially in view of the measures taken by governmental authorities regarding enforced lockdowns and social distancing. Traditional studies empirically explored the relationship between these important macroeconomic variables only for the short run and long run. Firstly, we employed the autoregressive distributed lag (ARDL) cointegration test and two causality tests (Granger causality and Toda-Yamamoto) to check the cointegration properties and causal relationship among these variables, respectively. After confirming the long-run causality from the ARDL bound test, we decomposed the time series of growth, inflation, and the interest rate into different time scales using wavelet analysis which allows us to study the relationship among variables for the very short run, medium run, long run, and very long run. The continuous wavelet transform (CWT), the cross-wavelet transform (XWT), cross-wavelet coherence (WTC), and multi-scale Granger causality tests were used to investigate the co-movement and nature of the causality between inflation and growth and the interest rate and growth. The results of the wavelet and multi-scale Granger causality tests show that the causal relationship between these variables is not the same across all time horizons; rather, it is unidirectional in the short-run and medium-run but bi-directional in the long-run. Therefore, this study suggests that the central bank should try to maintain inflation and the interest rate at a low level in the short run and medium run instead of putting too much pressure on these variables in the long-run.

In this paper, MODWT is used to decompose the Electrocardiography (ECG) signals and to identify the changes of R waves in the noisy input ECG signal. The MODWT is used to handle the arbitrary changes in the input signal. The R wave’s detctected by the proposed framework is used by the doctors and careholders to take necessary action for the patients. MATLAB simulink model is used to develop the simulation model for the MODWT method. The performance of the MODWT based remote health monitoring system method is comparatively analyzed with other ECG monitoring approaches such as Haar Wavelet Transformation (HWT) and Discrete Wavelet Transform (DWT). Sensitivity, specificity, and Receiver Operating Characteristic (ROC) curve are calculated to evaluate the proposed Internet of Things with MODWT based ECG monitoring system. We have used MIT-BIH Arrythmia Database to perform the experiments.

This paper is concerned with an end-to-end electrocardiogram (ECG) signal transformation from a continuous-wave (CW) radar signal using a specialized deep learning model. For this purpose, the presented deep learning model is designed using convolutional neural networks (CNNs) and bidirectional long short-term memory (Bi-LSTM) with a maximum-overlap discrete wavelet transform (MODWT) layer and an adaptive neuro-fuzzy network (ANFN) layer. The proposed method has the advantage of developing existing deep networks and machine learning to reconstruct signals through CW radars to acquire ECG biological information in a non-contact manner. The fully connected (FC) layer of the CNN is replaced by an ANFN layer suitable for resolving black boxes and handling complex nonlinear data. The MODWT layer is activated via discrete wavelet transform frequency decomposition with maximum-overlap to extract ECG-related frequency components from radar signals to generate essential information. In order to evaluate the performance of the proposed model, we use a dataset of clinically recorded vital signs with a synchronized reference sensor signal measured simultaneously. As a result of the experiment, the performance is evaluated by the mean squared error (MSE) between the measured and reconstructed ECG signals. The experimental results reveal that the proposed model shows good performance in comparison to the existing deep learning model. From the performance comparison, we confirm that the ANFN layer preserves the nonlinearity of information received from the model by replacing the fully connected layer used in the conventional deep learning model.

Structural vibration analysis often involves evaluating power spectral density to understand vibration processes. However, these spectra typically include overlapping vibration modes, complicating the analysis of individual components. This study presents a method to separate vibration modes into distinct components, simplifying structural vibration analysis. By combining maximal overlap discrete wavelet transform with fast Fourier transform, the composite vibration signal is decomposed into frequency-specific components. This approach enables precise analysis of individual vibration modes, facilitating the detection of those most sensitive to structural changes. Furthermore, the method effectively removes noise and irrelevant vibrations, enhancing the accuracy and reliability of structural evaluations.

Cardiovascular diseases are among the major global health problems. For example, sudden cardiac death (SCD) accounts for approximately 4 million deaths worldwide. In particular, an SCD event can subtly change the electrocardiogram (ECG) signal before onset, which is generally undetectable by the patient. Hence, timely detection of these changes in ECG signals could help develop a tool to anticipate an SCD event and respond appropriately in patient care. In this sense, this work proposes a novel computational methodology that combines the maximal overlap discrete wavelet packet transform (MODWPT) with stacked autoencoders (SAEs) to discover suitable features in ECG signals and associate them with SCD prediction. The proposed method efficiently predicts an SCD event with an accuracy of 98.94% up to 30 min before the onset, making it a reliable tool for early detection while providing sufficient time for medical intervention and increasing the chances of preventing fatal outcomes, demonstrating the potential of integrating signal processing and deep learning techniques within computational biology to address life-critical health problems.

Recently, the application of bio-signals in the fields of health management, human–computer interaction (HCI), and user authentication has increased. This is because of the development of artificial intelligence technology, which can analyze bio-signals in numerous fields. In the case of the analysis of bio-signals, the results tend to vary depending on the analyst, owing to a large amount of noise. However, when a neural network is used, feature extraction is possible, enabling a more accurate analysis. However, if the bio-signal time series is analyzed as is, the total neural network increases in size. In this study, to accomplish a light-weight neural network, a maximal overlap discrete wavelet transform (MODWT) and a smoothing technique are used for better feature extraction. Moreover, the learning efficiency is increased using an augmentation technique. In designing the neural network, a one-dimensional convolution layer is used to ensure that the neural network is simple and light-weight. Consequently, the light-weight attribute can be achieved, and neural networks can be implemented in edge devices such as the field programmable gate array (FPGA), yielding low power consumption, high security, fast response times, and high user convenience for wearable applications. The electromyogram (EMG) signal represents a typical bio-signal in this study.