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This paper uncover a new perception of the dynamic interconnection between CO 2 emission and economic growth, renewable energy use, trade openness, and technological innovation in the Portuguese economy utilizing innovative Morlet wavelet analysis. The research applied continuous wavelet transform, wavelet correlation, the multiple and partial wavelet coherence, and frequency domain causality analyses are applied on variables of investigation using dataset between 1980 and 2019. The result of these analyses disclosed that the interconnection among the indicators progresses over time and frequency. The present analysis finds notable wavelet coherence and significant lead and lag interconnections in the frequency domain, while conflicting relationships among the variables are found in the time domain. The wavelet analysis according to economic viewpoint affirms that renewable energy consumption helps to curb CO 2 while trade openness, technological innovation, and economic growth contribute to CO 2 . The outcomes also proposed that renewable energy consumption decreases CO 2 in medium and long run in Portugal. Therefore, policymakers in Portugal should stimulate investment in renewable energy sources, establish restrictive laws, and enhance energy innovation.

The study of wave-structure interactions involving nonlinear forces would often make use of the popular hybrid frequency–time domain method. In the hybrid method, the frequency-domain analysis could firstly provide the reliable and accurate dynamic parameters and responses; then these parameters and responses are transformed to the parameters to establishing the basic time-domain equation. Additionally, with the addition of the required linear and nonlinear forces, the time-domain analysis can be used to solve for the practical problems. However, the transformation from the frequency domain to the time domain is not straightforward, and the implementation of the time-domain equation could become increasingly complicated when different modes of motion are coupled. This research presents a systematic introduction on how to implement the time-domain analysis for floating structures, including the parameter transformations from the frequency domain to the time domain, and the methods for calculating and approximating the impulse functions and the fluid-memory effects, with special attention being paid to the coupling terms among the different motion modes, and the correctness of the time-domain-equation implementation. The main purpose of this article is to provide relevant information for those who wish to build their own time-domain analyses with the open-source hydrodynamic analysis packages, although commercial packages are available for time-domain analyses.

Four different applications of spectral proper orthogonal decomposition (SPOD) are demonstrated on large-eddy simulation data of a turbulent jet. These are: low-rank reconstruction, denoising, frequency–time analysis and prewhitening. We demonstrate SPOD-based flow-field reconstruction using direct inversion of the SPOD algorithm (frequency-domain approach) and propose an alternative approach based on projection of the time series data onto the modes (time-domain approach). We further present a SPOD-based denoising strategy that is based on hard thresholding of the SPOD eigenvalues. The proposed strategy achieves significant noise reduction while facilitating drastic data compression. In contrast to standard methods of frequency–time analysis such as wavelet transform, a proposed SPOD-based approach yields a spectrogram that characterises the temporal evolution of spatially coherent flow structures. A convolution-based strategy is proposed to compute the time-continuous expansion coefficients. When applied to the turbulent jet data, SPOD-based frequency–time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events. This work suggests that the time-domain approach is preferable for low-rank reconstruction of individual snapshots, and the frequency-domain approach for denoising and frequency–time analysis.

In condition based maintenance, different signal processing techniques are used to sense the faults through the vibration and acoustic emission signals, received from the machinery. These signal processing approaches mostly utilise time, frequency, and time-frequency domain analysis. The features obtained are later integrated with the different machine learning techniques to classify the faults into different categories. In this work, different statistical features of vibration signals in time and frequency domains are studied for the detection and localisation of faults in the roller bearings. These are later classified into healthy, outer race fault, inner race fault, and ball fault classes. The statistical features including skewness, kurtosis, average and root mean square values of time domain vibration signals are considered. These features are extracted from the second derivative of the time domain vibration signals and power spectral density of vibration signals. The vibration signal is also converted to the frequency domain and the same features are extracted. All three feature sets are concatenated, creating the time, frequency and spectral power domain feature vectors. These feature vectors are finally fed into the K- nearest neighbour, support vector machine and kernel linear discriminant analysis for the detection and classification of bearing faults. With the proposed method, the reduction percentage of more than 95% percent is achieved, which not only reduces the computational burden but also the classification time. Simulation results show that the signals are classified to achieve an average accuracy of 99.13% using KLDA and 96.64% using KNN classifiers. The results are also compared with the empirical mode decomposition (EMD) features and Fourier transform features without extracting any statistical information, which are two of the most widely used approaches in the literature. To gain a certain level of confidence in the classification results, a detailed statistical analysis is also provided.

Tool wear monitoring has been increasingly important in intelligent manufacturing to increase machining efficiency. Multi-domain features can effectively characterize tool wear condition, but manual feature fusion lowers monitoring efficiency and hinders the further improvement of predicting accuracy. In order to overcome these deficiencies, a new tool wear predicting method based on multi-domain feature fusion by deep convolutional neural network (DCNN) is proposed in this paper. In this method, multi-domain (including time-domain, frequency domain and time–frequency domain) features are respectively extracted from multisensory signals (e.g. three-dimensional cutting force and vibration) as health indictors of tool wear condition, then the relationship between these features and real-time tool wear is directly established based on the designed DCNN model to combine adaptive feature fusion with automatic continuous prediction. The performance of the proposed tool wear predicting method is experimentally validated by using three tool run-to-failure datasets measured from three-flute ball nose tungsten carbide cutter of high-speed CNC machine under dry milling operations. The experimental results show that the predicting accuracy of the proposed method is significantly higher than other advanced methods.

Purpose To assess the validity of RR intervals and short-term heart rate variability (HRV) data obtained from the Polar V800 heart rate monitor, in comparison to an electrocardiograph (ECG). Method Twenty participants completed an active orthostatic test using the V800 and ECG. An improved method for the identification and correction of RR intervals was employed prior to HRV analysis. Agreement of the data was assessed using intra-class correlation coefficients (ICC), Bland–Altman limits of agreement (LoA), and effect size (ES). Results A small number of errors were detected between ECG and Polar RR signal, with a combined error rate of 0.086 %. The RR intervals from ECG to V800 were significantly different, but with small ES for both supine corrected and standing corrected data (ES <0.001). The bias (LoA) were 0.06 (−4.33 to 4.45 ms) and 0.59 (−1.70 to 2.87 ms) for supine and standing intervals, respectively. The ICC was >0.999 for both supine and standing corrected intervals. When analysed with the same HRV software no significant differences were observed in any HRV parameters, for either supine or standing; the data displayed small bias and tight LoA, strong ICC (>0.99) and small ES (≤0.029). Conclusions The V800 improves over previous Polar models, with narrower LoA, stronger ICC and smaller ES for both the RR intervals and HRV parameters. The findings support the validity of the Polar V800 and its ability to produce RR interval recordings consistent with an ECG. In addition, HRV parameters derived from these recordings are also highly comparable.

Abstract Study Objectives Patients with obstructive sleep apnea (OSA) exhibit heterogeneous heart rate variability (HRV) during wakefulness and sleep. We investigated the influence of OSA severity on HRV parameters during wakefulness in a large international clinical sample. Methods 1247 subjects (426 without OSA and 821 patients with OSA) were enrolled from the Sleep Apnea Global Interdisciplinary Consortium. HRV parameters were calculated during a 5-minute wakefulness period with spontaneous breathing prior to the sleep study, using time-domain, frequency-domain and nonlinear methods. Differences in HRV were evaluated among groups using analysis of covariance, controlling for relevant covariates. Results Patients with OSA showed significantly lower time-domain variations and less complexity of heartbeats compared to individuals without OSA. Those with severe OSA had remarkably reduced HRV compared to all other groups. Compared to non-OSA patients, those with severe OSA had lower HRV based on SDNN (adjusted mean: 37.4 vs. 46.2 ms; p < 0.0001), RMSSD (21.5 vs. 27.9 ms; p < 0.0001), ShanEn (1.83 vs. 2.01; p < 0.0001), and Forbword (36.7 vs. 33.0; p = 0.0001). While no differences were found in frequency-domain measures overall, among obese patients there was a shift to sympathetic dominance in severe OSA, with a higher LF/HF ratio compared to obese non-OSA patients (4.2 vs. 2.7; p = 0.009). Conclusions Time-domain and nonlinear HRV measures during wakefulness are associated with OSA severity, with severe patients having remarkably reduced and less complex HRV. Frequency-domain measures show a shift to sympathetic dominance only in obese OSA patients. Thus, HRV during wakefulness could provide additional information about cardiovascular physiology in OSA patients. Clinical Trial Information:  A Prospective Observational Cohort to Study the Genetics of Obstructive Sleep Apnea and Associated Co-Morbidities (German Clinical Trials Register - DKRS, DRKS00003966) https://www.drks.de/drks_web/navigate.do?navigationId=trial.HTML&TRIAL_ID=DRKS00003966

In the fault diagnosis of rotating machinery, vibration signal or spectrum is usually used. As a data-driven method, deep learning has been introduced into the field of fault diagnosis. But it often confronts with two critical difficulties: few fault cases and single data source. To this end, we employ the prototype network to solve the problem of few fault cases, and use the two-branch technique to combine data sources in time domain and frequency domain. We introduce the two-branch network structure into the framework of the prototype network and develop a two-branch prototype network (TBPN) for fault diagnosis. The TBPN model is constructed through three main steps. First, we extract information from vibration signals in time domain and frequency domain respectively, and feed them into the model as two branches. Second, the prototype representation of each fault in time domain and frequency domain can be learned through metric learners, and the distances between fault prototypes and query faults features are then calculated. Third, the distances in time domain and frequency domain are integrated and incorporated into the softmax function for multi-classification. The performance of TBNP is verified by a real-world application on fault diagnosis of rotating machinery with the case data accumulated by an industrial Internet enterprise in China. The results show that the TBPN model is suitable for fault diagnosis in the case of small data. Compared with using time domain signals or spectrum alone, their combination use can improve the effectiveness of fault diagnosis.

Fault diagnosis is an important means to ensure the safe and reliable operation of mechanical equipment. In machinery fault diagnosis, collecting and mining the potential fault information of the vibration signal is the most commonly used method to reflect the operating status of the equipment. In engineering scenarios, in the face of rotating machinery with variable speed, simple time domain analysis or frequency domain analysis is difficult to solve the problem. The time-frequency analysis technology that combines time-frequency transformation and data analysis can solve practical engineering problems by capturing the transient information of the signal. At present, a large number of related literatures have been published in academic journals. This paper hopes to provide convenience for relevant researchers and motivate researchers to further explore by summarizing the published literature. First, this paper briefly explains the concept of time-frequency analysis and its development. Then, the time-frequency transformation method proposed for the characteristics of rotating machinery fault vibration signal and related works of literature are reviewed, and the key issues of the application of time-frequency transformation method in rotating machinery fault diagnosis are discussed. Next, this paper summarizes the relevant literature on the combination of data analysis technology and time-frequency transformation and sorts out its development route and prospects. The study reveals that time-frequency analysis technology is able to detect the rotating machinery fault effectively. The time-frequency analysis technology has made abundant achievements in the field of rotating machinery fault diagnosis. It is expected that this review would inspire researchers to explore the potential of time-frequency analysis as well as to develop advanced research in this field.

In this paper, we propose to use time-domain transient analysis to compute the response of structures in a wide frequency band by means of Fourier transform. A time-domain adjoint variable method is then developed to carry out the sensitivity analysis of frequency-domain objective functions. By using the concept of frequency response function, it turns out that both the objective function and its sensitivity information at multiple frequencies can be obtained by one original simulation and at most one adjoint simulation, respectively. It is also demonstrated that some commonly used performance indices, e.g., dynamic compliance and input power, are indeed self-adjoint; thus, no extra adjoint simulations are needed, which makes the sensitivity analysis extremely efficient. An obvious distinction between the proposed method and the traditional frequency domain methods is that in our method, the frequency response curves in a wide band can be obtained in each iteration with no extra costs. It follows that it is easy to track the evolution of the frequency response curve in our method, which is essential in both computational and engineering sense. Several numerical examples are tested to show the effectiveness of the proposed method.