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A single type of signal processing means that it is difficult to analyze vibration signals comprehensively and effectively. By comprehensively using wavelet analysis techniques, a comprehensive and in-depth study of aero-engine vibration conditions is realized as a way to carry out health management. By introducing various types of wavelet analysis techniques and using Labview2022 programming, corresponding signal processing tools are developed for the analysis of the collected vibration signals. The comprehensive analysis of aero-engine vibration signals based on the wavelet transform method is realized, and the corresponding products are successfully applied in engineering practice.

As a part of the earthquake ground motion, large velocity pulses are probably one of the important factors leading to serious rock structural damage and geological disasters. It is vitally important to identify the response characteristics of large-scale structures under near-field pulse-like ground motions for earthquake prevention and disaster reduction. In this study, the pulse parameters from the 1999 Chi-Chi and 2018 Hualien earthquakes are extracted using the wavelet transform method, and the potential consequences of velocity pulses on the seismic response of the buildings are assessed. Our results show that the near-field ground motions affected by the directivity effect contain some rich large pulse contents in the velocity time histories. The Chi-Chi earthquake presents a more obvious directivity effect than the Hualien earthquake, and the near-field velocity pulses are closely related to the severely damaged structures. The potential damage of both earthquakes to high-rise buildings can be evaluated by the relationship between the characteristic period of the velocity pulse and the fundamental natural period of the engineering structure. By comparing the periods, it can be revealed that some long-period spectral values in the range of 0.8–3.0 s exceed the seismic design values in the vicinity of the causative faults, and the vulnerability of high-rise buildings against pulse-like ground motions in the Chi-Chi earthquake is stronger than that in the Hualien earthquake. Interestingly, the ratio of peak ground velocity to acceleration (PGV/PGA) and maximum pseudo response velocity (PSV) are suitable as seismic intensity indicators of pulse-like ground motions, which can reflect the rupture direction of source characteristic and site amplification of near-surface soft deposition area around the causative fault. This study provides some references for seismic hazard assessment and post-earthquake structural design.

One of the basic features of solar activity is the quasi-biennial oscillations (QBOs)—variations with a period of about two years. The nature of the QBO remains unclear and the most puzzling is the high instability of the QBO period. We investigated a fine structure of the QBO period variability as manifested in sunspot area variations in Solar Cycles 19 – 23 using the wavelet transform with a real mother wavelet, Daubechies 10, that provided a high temporal resolution. We found that within every 11-yr solar cycle the QBO period varies not randomly, as it is widely accepted now, but it gradually decreases from the beginning of the solar cycle till the end, in phase with the shift of the average sunspots latitude to the equator. We have analyzed in a similar way the time series which were simulated using a combination of sine waves with different periods (constant and variable one) and red noise with a standard deviation as large as 40% of the sine amplitude. The analysis has shown that noise does not distort significantly the initial signal and noise itself does not form the structures with the properties which were observed in the case of the natural time series. We suppose that the revealed modification of the QBO period with the development of the solar cycle may be related to the latitudinal differential rotation in the solar convection zone and the possible influence of the rotational velocity in the region of the QBO generation on the QBO period value. Under this assumption, the process responsible for the QBO generation should operate in a layer with a substantial latitudinal shear which according to the helioseismology analysis is observed in the bulk of the convection zone and is getting smaller in the vicinity of the tachocline.

Partial discharge (PD) is a symptom of insulation defect or degradation in high-voltage equipment. Thus, PD detection is an important diagnostic tool. Furthermore in practical situations, the PD can be generated from a single or multiple sources. Being able to detect and classify such PD events will help to determine the necessary corrective action to prevent insulation breakdown. To demonstrate, three different simulated discharge conditions in transformers were investigated: void, floating metal and their combination. The PD signals were captured using an ultra-high frequency (UHF) sensor and denoised using wavelet transform method by application of Matlab wavelet multi-variate denoising tool. Two types of mother wavelet, that is, db and sym, were applied to decompose the signals and extract the signal features in terms of their skewness, kurtosis and energy. These features were then used as input to train a neural network to analyse and determine the PD source type. Results show this technique is able to classify and recognise single and multiple PD source types with a high degree of success.

Application of time–time (TT)-transform for differential protection of power transformers has been suggested. At first, external and internal disturbances are discriminated. If the disturbance is external, relay scheme restrains more analysis and tripping. Otherwise, the differential current signal is analysed by TT-transform and TT-matrix is computed. Next, a suggested index is computed, accordingly. Discrimination between inrush current and internal fault is performed by the proposed index. To investigate the effectiveness of the method, a typical power system has been modelled in EMTP software. Also, the relay scheme has been developed in MATLAB environment. Then, differential currents extracted from the system modelled in EMTP have been fed to MATLAB for analysis. Also, the performance of the method in noisy environments has been assessed. To make an analogy between the TT-transform-based method and wavelet transform-based methods, a wavelet transform-based scheme has been developed in MATLAB environment and results have been compared to the results of the TT-transform-based method. In addition, an S-transform-based method has been implemented in MATLAB and has been compared with the suggested method. The results show that the method is superior to both wavelet transform and S-transform-based methods.

The planetary boundary layer (PBL) height is a key variable in climate modeling and has an enormous influence on air pollution. A method based on the wavelet covariance transform (WCT) applied to lidar data is tested in this paper as an automated and non‐supervised method to obtain the PBL height. The parcel and the Richardson number methods applied to radiosounding data and the parcel method applied to microwave radiometer temperature profiles are used as independent measurements of the PBL height in order to optimize the parameters required for its detection using the WCT method under different atmospheric conditions. This optimization allows for a one‐year statistical analysis of the PBL height at midday over Granada (southeastern Spain) from lidar data. The PBL height showed a seasonal cycle, with higher values in summer and spring while lower values were found in winter and autumn. The annual mean was 1.7 ± 0.5 km a.s.l. during the study period. The relationship of the PBL height with aerosol properties is also analyzed for the one‐year period. Key Points This study uses the WCT to determine automatically mixing height from lidar data The method was optimized comparing with radiosoundings and microwave radiometer One year analysis of the PBL height is done, correlating with aerosol properties

Atmospheric boundary layer height (ABLH) was observed by the CHM15k ceilometer (January 2008 to October 2013) and the PollyXT lidar (July 2013 to December 2018) over the European Aerosol Research LIdar NETwork to Establish an Aerosol Climatology (EARLINET) site at the Remote Sensing Laboratory (RS-Lab) in Warsaw, Poland. Out of a maximum number of 4017 observational days within this period, a subset of quasi-continuous measurements conducted with these instruments at the same wavelength (1064 nm) was carefully chosen. This provided a data sample of 1841 diurnal cycle ABLH observations. The ABLHs were derived from ceilometer and lidar signals using the wavelet covariance transform method (WCT), gradient method (GDT), and standard deviation method (STD). For comparisons, the rawinsondes of the World Meteorological Organization (WMO 12374 site in Legionowo, 25 km distance to the RS-Lab) were used. The ABLHs derived from rawinsondes by the skew-T-log-p method and the bulk Richardson (bulk-Ri) method had a linear correlation coefficient (R2) of 0.9 and standard deviation (SD) of 0.32 km. A comparison of the ABLHs obtained for different methods and instruments indicated a relatively good agreement. The ABLHs estimated from the rawinsondes with the bulk-Ri method had the highest correlations, R2 of 0.80 and 0.70 with the ABLHs determined using the WCT method on ceilometer and lidar signals, respectively. The three methods applied to the simultaneous, collocated lidar, and ceilometer observations (July to October 2013) showed good agreement, especially for the WCT method (R2 of 0.94, SD of 0.19 km). A scaling threshold-based algorithm was proposed to homogenize ceilometer and lidar datasets, which were applied on the lidar data, and significantly improved the coherence of the results (R2 of 0.98, SD of 0.11 km). The difference of ABLH between clear-sky and cloudy conditions was on average below 230 m for the ceilometer and below 70 m for the lidar retrievals. The statistical analysis of the long-term observations indicated that the monthly mean ABLHs varied throughout the year between 0.6 and 1.8 km. The seasonal mean ABLH was of 1.16 ± 0.16 km in spring, 1.34 ± 0.15 km in summer, 0.99 ± 0.11 km in autumn, and 0.73 ± 0.08 km in winter. In spring and summer, the daytime and nighttime ABLHs appeared mainly in a frequency distribution range of 0.6 to 1.0 km. In winter, the distribution was common between 0.2 and 0.6 km. In autumn, it was relatively balanced between 0.2 and 1.2 km. The annual mean ABLHs maintained between 0.77 and 1.16 km, whereby the mean heights of the well-mixed, residual, and nocturnal layer were 1.14 ± 0.11, 1.27 ± 0.09, and 0.71 ± 0.06 km, respectively (for clear-sky conditions). For the whole observation period, the ABLHs below 1 km constituted more than 60% of the retrievals. A strong seasonal change of the monthly mean ABLH diurnal cycle was evident; a mild weakly defined autumn diurnal cycle, followed by a somewhat flat winter diurnal cycle, then a sharp transition to a spring diurnal cycle, and a high bell-like summer diurnal cycle. A prolonged summertime was manifested by the September cycle being more similar to the summer than autumn cycles.

We analyzed the planetary boundary layer (PBL) characteristics in Warsaw, Poland for a day of summer, autumn, winter, and spring of 2021 by integrating and comparing measured and simulated data. Using remote sensing lidar sensor data, the PBLH was calculated using wavelet covariance transform (WCT) and the gradient method (GM). Also, simulations of turbulent fluxes were performed utilizing the large eddy simulation (LES) from the Parallel Large Eddy Simulation Model (PALM) to better understand how turbulence and convection behave across different seasons in Warsaw. The PBLH diurnal cycles showed pronounced changes in their vertical structure as a function of the season: the winter heights were shallow (~0.7 km), while summer heights were deeper (~1.7 km). The spring and autumn presented transient characteristics of PBLH around 1.0 km. This study is crucial for enhancing urban air quality and climate modeling. The PBLH simulations from PALM showed agreement with the measured data, with an underestimation of approximately 10% in both methods. Through PALM, it was possible to observe that summer exhibited increased convection, enhanced mixing efficiency, and a deeper boundary layer compared to other seasons throughout the daily cycle. Winter has a lower sensible heat flux and little convection throughout the day. Spring and autumn showed intermediate characteristics. In this way, the effectiveness of the applicability of the PALM model to obtain flows within the PBL and their heights is highlighted, because correlations ranged from strong to very strong (r ≥ 0.70).

Capacitive micromachined ultrasonic transducers (CMUTs) are microelectromechanical systems used for the generation of ultrasounds. The fundamental element of the transducer is a clamped thin metallized membrane that vibrates under voltage variations. To control such oscillations and to optimize its dynamic response it is necessary to know the modal parameters of the membrane such as resonance frequency, damping and stiffness coefficients. The purpose of this work is to identify these parameters using only the time data obtained from the membrane center displacement. Dynamic measurements are conducted in time domain and we use two methods to identify the modal parameters: a subspace method based on an innovation model of the state-space representation and the continuous wavelet transform method based on the use of the ridge of the wavelet transform of the displacement. Experimental results are presented showing the effectiveness of these two procedures in modal parameter identification.

Certain parts of a wind turbine, for example, the gearbox require significant time and heavy lifting equipment in the event of catastrophic failure necessitating replacement. Continuous condition monitoring has the potential to catch problems early, enable scheduled preventative maintenance and thereby reduce turbine downtime, reduce the number of site visits and prevent secondary damage. Accelerometers applied to mechanical components of the drive train are traditionally used for condition monitoring, but require their own data acquisition system and analysis software. In contrast, the electrical current and voltage are continuously measured and could also be used for condition monitoring more cheaply. An experimental data acquisition system has been installed on a small (25 kW) onshore turbine in Leicestershire, UK to compare three-phase currents and voltages on the stator windings with six accelerometer signals. Data have been recorded before and after a gearbox failure and replacement. Data were analysed using both Fourier transform and Morlet continuous wavelet transform methods. Results show that the stator voltages show the same radial and axial mode vibration frequencies as the accelerometers, and could therefore be used for condition monitoring. Furthermore, the stator currents show torsional modes of vibration not picked up by the accelerometers.