Complex Frequency Research Articles

Parametric channel estimation for RIS-assisted mmWave MIMO-OFDM systems with low pilot overhead

We consider the channel estimation problem in a millimeter-wave (mmWave) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system aided by a passive reconfigurable intelligent surface (RIS). Initially, leveraging the inherent sparsity of mmWave channels, we decouple the channel estimation into the recovery of multipath parameters, including spatial frequencies of angles, delays, and complex gains. Subsequently, we employ two training schemes: the first involves a full row rank constrained RIS phase shift pattern, and the second incorporates a Kronecker structure constrained RIS phase shift pattern. These schemes reform channel estimation into estimating parameters from two fifth-order tensor signals, which admit constrained Canonical Polyadic decomposition. Moreover, both tensor signals share Vandermonde-constrained factor matrices, enabling algebraic algorithms for tensor decomposition problems and recovering channel multipath parameters. Theoretical analyses show that the first training scheme has a lower signal processing complexity for channel estimation, while the second attains a higher estimation accuracy. Also, we prove that our proposed two schemes have the same minimum pilot overhead, which is as low as proportional to the product of the number of paths in the two MIMO channels (transmitter-RIS and RIS-receiver). Numerical results validate the effectiveness of our proposed methods.

Compression and self-compression of frequency modulated spherical photon density waves in anisotropic scattering media

We report on the results of a simulation of the photon density waves with pulse amplitude modulation by a complex frequency modulated signal. The problem is considered for the optical properties typical for sea water with anisotropy factor values varying from 0.75 to 0.93 at source-detector distances up to 120 m. It is shown that multiple scattering in a medium does not prevent effective compression of a signal registered using matched detection. Two competing phenomena affecting the detected pulse duration and depending on the central frequency of the modulation signal are discussed. The effect of faster attenuation of high harmonics in a complexly modulated signal leads to the detected signal duration increase as a consequence of multiple scattering. On the other hand, anomalous dispersion of photon density waves in media with scattering anisotropy leads to the pulse self-compression. The simulation results presented in the paper demonstrate the prevalence of different phenomena depending on the central frequency of the modulation signal resulting in a pulse duration decrease or increase in different frequency ranges covering the band from 107 to 2⋅109 Hz. The effect of the phase function shape on the observed effect is also discussed.

Quantitative Fault Diagnosis of Planetary Gearboxes Based on Improved Symbolic Dynamic Entropy

To realize a quantitative diagnosis of faults in the planetary gearboxes of wind turbines by processing the complex frequency signals of the planetary gear boxes and avoiding the aliasing problem of the resulting frequencies, this paper proposes a diagnosis method based on improved variational mode decomposition (IVMD) and average multi-scale double symbolic dynamic entropy (AMDSDE). Moreover, an IVMD algorithm based on multi-scale permutation entropy is introduced to reduce noise interference and realize signal demodulation. Considering the effects of complex transfer paths and the correlation between current and adjacent state modes, AMDSDE is proposed. Each fault size is obtained based on the entropy curve, and the AMDSDE of unknown faults is calculated. To verify the accuracy of the proposed method, simulations and experimental signals are processed. The quantitative diagnosis of the planetary gearboxes of wind turbines is realized, providing a reliable basis for evaluating the health status of planetary gearboxes.

Rethinking general time series analysis from a frequency domain perspective

Recently, Transformers and MLPs based models have dominated and made significant progress in time series analysis. However, these methods struggle to capture the complete periodic features to model the global dependencies of time series. To this end, we provide a new perspective to explore the potential of time series in the frequency domain. Specifically, we propose the DFT-based Amplitude-Phase Decoupling Network (APDNet), which learns the significance changes and periodicity characteristics of time series by decoupling the real and imaginary parts in the complex frequency domain. First, we propose the Fourier Temporal/Variable Interaction Module to model time dependency and dependency multiple variables, respectively. Secondly, we innovatively propose the Dimensional Expanded Feature Embedding Module (DEFEM), which expands time series into a higher-dimensional representation space to preserve more independent features. Finally, through extensive experiments on multiple real-world datasets, our APDNet achieves state-of-the-art performance in various tasks such as long-term and short-term forecasting, anomaly detection, imputation, and classification. Code is available at: https://github.com/CodeJester196/APDNet.

Modeling Hybrid AC/DC Power Systems With the Complex Frequency Concept

Modeling Hybrid AC/DC Power Systems With the Complex Frequency Concept

3D Marine Controlled-Source Electromagnetic Numerical Simulation Considering Terrain and Static Effect

The marine controlled-source electromagnetic (CSEM) method is an important geophysical method for the exploration of marine hydrocarbon resources. In marine CSEM forward modeling the uplift terrain, such as submarine hills and seamounts, the static effects caused by polymetallic nodules and hydrothermal sulfide are ignored which can lead to the deviation of marine CSEM data. To improve the accuracy of data processing and interpretation, this study realizes efficient 3D numerical simulation considering submarine uplift terrain and static effect based on the finite difference (FD) algorithm in a fictitious wave domain. First, based on the correspondence principle between the fictitious wave domain and a real diffusive domain, we derive the FD electromagnetic field iteration equations of the fictitious wave domain, and apply the fictitious emission source and the boundary condition of complex frequency shifted-perfectly matched layer (CFS-PML). We use the inverse transformation method to convert the electromagnetic response to the diffusive domain. Then, we carry out simulations on typical 1D and 3D reservoir models to verify the correctness and effectiveness of the algorithm. Furthermore, we design an uplift terrain model and a static effect model and study the influence of parameters such as top width, bottom width, height and volume of uplift terrain on the CSEM field response characteristics through the forward modeling of multiple models and discuss the influence of parameters such as electrical conductivity, length, width, thickness, depth and volume of a shallow anomaly on the marine CSEM response. Finally, we analyze the characteristics and rules of electromagnetic field propagation of uplift terrain and static effect, which provides theoretical guidance for the design of marine CSEM exploration systems.

Complex frequency divider

This work presents the Complex Frequency Divider Formula (CFDF), an explicit equation for the complex frequencies (CFs) of the voltage of every bus of a power system in terms of a linear combination of the CFs of the currents injected by the devices connected to the network. The coefficients of this linear combination depend on the topology of the system, voltages and currents. The CFDF carries valuable information on the impact of every device on the dynamic of the voltage and frequency of any particular bus of the system. The formulation is exact, as it does not require any simplification of the dynamic model of the system. The CFDF is implemented in two benchmark systems to show its potential in static and dynamic analysis in different scenarios. Finally, relevant notes on the applications of the proposed formula are outlined.

Exploring temperature effects on raw polysaccharide in semi-diluted solution using complex conductivity: Correlation analysis of activation energies

The evolution of the complex conductivity of raw polysaccharides extracted from Cystoseira myriophyloides algae exhibited significant temperature dependence in an aqueous solution. An analysis of the complex conductivity versus frequency was conducted using an appropriate electrical circuit based on our theoretical approach. This facilitated the generation of analytical functions representing the relaxation processes occurring at different temperatures. Subsequently, extrapolation and deconvolution procedures were employed to further investigate and identify all relaxation processes and their origins. These approaches revealed the presence of three relaxation processes. The first relaxation, observed at low frequency, is attributed to interfacial polarization between the electrode and the solution. The second and third relaxations, observed at medium and high frequencies, are attributed to bulk relaxation processes. Then, subtracting the low-frequency process clarified the bulk relaxation processes. Both relaxations are described by the Cole-Cole relaxation, which effectively models the well-known Maxwell-Wagner-Sillars (MWS) phenomenon typically observed in polyelectrolyte solutions. This relaxation is typically caused by interfacial polarization between molecular chains and counterions in the sample. Both relaxations were found to be thermally activated. The temperature dependence of useful parameters extracted from each relaxation, such as relaxation time (τσ) and conductivity (σdc) and (σ∞), followed Arrhenius law behavior. Furthermore, activation energy values for each relaxation process were determined, establishing a linear correlation between activation energy values related to relaxation time (τσ) and both conductivities (σdc) and (σ∞). These results confirm the origin of bulk relaxations and demonstrate a strong link between relaxation and conduction mechanisms.

The Energy Circuit of the Exhaust Gas Heat Recovery Circuit of a 25 kW Diesel Generator

The purpose of the work is to describe the installation using differential equations and obtain approximate values before the experiment. In this paper, a constructive scheme of the experimental device is proposed, and the principle of its operation is described in detail. The power circuit of the device has been drawn up. Complex impedance, frequency function, amplitude-frequency characteristic and phase-frequency characteristic are obtained by mathematical transformation of the power circuit. The frequency response of the circuit is constructed. As a result of the calculations, we will obtain the amplitude frequency response and the phase frequency response. Using the found values of the characteristics, we will build graphs and draw conclusions about how the characteristics depend on the change in parameters and why the graph lines of the graphs are exactly the way they are.

Energy Circuit of a Thermal Circuit with a Direct-acting Regulator with a Capacity of 1 MW in Pulsating Mode

The purpose of the work is to describe the installation using differential equations and obtain approximate values before the experiment. In this paper, a constructive scheme of the experimental device is proposed, and the principle of its operation is described in detail. The power circuit of the device has been drawn up. Complex impedance, frequency function, amplitude-frequency characteristic and phase-frequency characteristic are obtained by mathematical transformation of the power circuit. The frequency response of the circuit is constructed. As a result of the calculations, we will obtain the amplitude frequency response and the phase frequency response. Using the found values of the characteristics, we will build graphs and draw conclusions about how the characteristics depend on the change in parameters and why the graph lines of the graphs are exactly the way they are.

Study of a Laboratory Circuit with a Warm Baseboard in Pulse Mode

The increasing global energy demand is a problem that people have been paying attention to, people's demand for energy is increasingly urgent, and improving energy efficiency has become a hot topic in this century. Studies have shown that pulsating flow has an important effect on heat transfer, and it has been concluded in most literatures that turbulent pulsation can enhance heat transfer in different degrees. Pulsation heat transfer is a comprehensive heat transfer process, and the best heat transfer performance can be achieved only when the thermal resistance of each part is reasonably coordinated. Based on the principle of hydraulic shock, this paper develops a device with warm substrate which can be used to increase the pulsating pressure and enhance the heat transfer efficiency of pulsating flow. Firstly, the construction scheme of the experimental device is proposed, and the working principle of the experimental device is described in detail. The complex impedance, frequency function, amplitude-frequency characteristic and phase-frequency characteristic are obtained by mathematical transformation of power supply circuit. Finally, the frequency response of the circuit is constructed.

Development of a Prototype Non-volatile Heating Circuit with Pulsating Mode

The emergence of global energy crisis makes energy saving technology become the key technology of sustainable development. Enhanced heat transfer technology can improve the efficiency of various heat transfer equipment and reduce the weight and volume, which plays a vital role in energy saving and sustainable economic development. In recent years, based on theoretical and experimental research, Chinese researchers and technicians have developed many new technologies to strengthen heat transfer, such as cross-scaled elliptic tube, discontinuous double-inclined inner rib tube, spiral groove tube, spiral groove tube, inner fin tube, twisted elliptic tube and so on. Among them, the pulsating heat transfer technology is an efficient and energy-saving means that can significantly strengthen the convective transport operation and improve the heat transfer effect. Through fluid pulsation or the vibration of the heat transfer pipe, the technology can remove the dirt deposited on the heat exchange surface, reduce the thermal resistance of the dirt, and improve the performance and life of the heat exchanger. It is widely used in the cooling of electronic components, automobile turbines, and the utilization of atomic energy in Marine environment. Firstly, the construction scheme of the experimental device is proposed, and the working principle of the experimental device is described in detail. The complex impedance, frequency function, amplitude-frequency characteristic and phase-frequency characteristic are obtained by mathematical transformation of power supply circuit. Finally, the frequency response of the circuit is constructed.

Dispersive behavior of SH waves in a smart composite structure of viscoelastic media

This study focuses on the dispersive behavior of SH waves in a piezoelectric viscoelastic (PV) layer sandwiched between a magnetoelastic fiber-reinforced viscoelastic (MFRV) layer and a heterogeneous viscoelastic half-space. The linear variation of the downward-pointing space variable introduces inhomogeneity in the viscoelastic half-space. With the help of the variable separation technique, the governing equations of the present model are solved to obtain solutions for the mechanical displacement and electric potential function. A complex frequency equation for the SH waves has been derived by applying appropriate boundary conditions. The results are confirmed by comparison to the classical case of Love wave, and special cases of the problem are also discussed. In the fundamental analytical study, two cases of the PV layer are discussed, and the effects of physical parameters on the phase and damped velocity of SH waves are investigated through numerical calculations and presented graphically. A comparative study has also been carried out to analyze the effects of the viscoelastic parameters, reinforcement parameters, thickness ratio parameter, magnetoelastic coupling parameter, inhomogeneity parameter, and the angle at which the wave intersects the magnetic field on the phase and damped velocity by taking electrically open and short conditions.

Equilibrium optimiser tuned frequency-shifted internal model control proportional-derivative decoupled dual-loop design for industrial plants followed by experimental validation

Integrating and unstable processes require rugged control demand by virtue of their non-self-regulation character. The occurrence of system poles located at the origin and on the right half of the complex frequency plane causes instability in an open-loop configuration. When these processes proceed with dead time, it demands more sophisticated control requirements. Therefore, binal-loop control schemes are recommended over single-loop controller schemes. For plants with prevalent unstable and integrating dynamics and dead time, a novel modified inferred internal model control-proportional derivative decoupled binal-loop control system is suggested. The inner-loop is controlled by the stabilising proportional derivative controller with Routh–Hurwitz stability constraints. The outer-loop contains an inferred internal model controller for reference-point tracking. The equilibrium optimiser is then used to minimise the integral squared error by tuning the inner and outer-loop controller settings in the confined search space. The suggested strategy delivers appreciable enhancement in the quantitative performance measures as compared to some of the contemporary control techniques. The effect of time-varying disturbance and robust stability analysis is also presented. Finally, utilising a magnetic levitation laboratory setup, the suggested method is experimentally verified using the hardware-in-loop method.

Charge superradiance on charged BTZ black holes

We study superradiant scattering for a charged scalar field subject to Robin (mixed) boundary conditions on a charged BTZ black hole background. Scalar field modes having a real frequency do not exhibit superradiant scattering, independent of the boundary conditions applied. For scalar field modes with a complex frequency, no superradiant scattering occurs if the black hole is static. After exploring some regions of the parameter space, we provide evidence for the existence of superradiantly scattered modes with complex frequencies for a charged and rotating BTZ black hole. Most of the superradiantly scattered modes we find satisfy Robin (mixed) boundary conditions, but there are also superradiantly scattered modes with complex frequencies satisfying Dirichlet and Neumann boundary conditions. We explore the effect of the black hole and scalar field charge on the outgoing energy flux of these superradiantly scattered modes, and also investigate their stability.

Effects of Operational and Environmental Conditions on Estimated Dynamic Characteristics of a Large In-service Wind Turbine

Abstract Purpose The reliable and continuous operation of wind turbines is of utmost importance, making it necessary to thoroughly understand their dynamic behavior under various operational and environmental conditions. Methods To achieve this, a data acquisition system distributed throughout the tower height is designed. The system records data such as the acceleration, temperature, and relative humidity from the sensors, along with the rotor speed, wind speed, temperature, pitch angle, nacelle direction, and wind direction from the data acquisition system of the turbine. The acquired data is synchronized and processed by Autonomous and Continuous System Identification system based on the poly-reference Least Squares Complex Frequency method. The extensive dataset, gathered over a 7-month period, allows for the estimation of modal parameters of the wind turbine. The modal parameters are then correlated with the operational and environmental conditions that were recorded. The relationships between these conditions are thoroughly analyzed and explained. Additionally, the operational principles of the wind turbine are elucidated in detail. The correlations between the modal parameters and operational or environmental factors are presented and interpreted, shedding light on the complex interplay between wind turbine dynamics and external conditions. Conclusion It can be said that changes in operational and environmental conditions affect the modal parameters of the wind turbine differently across various structural modes. Without considering these effects, structural health monitoring systems may produce false alarms. Failure to consider these effects in the development of structural health monitoring systems may lead to incorrect damage alarms.

Magnetic loss versus temperature and role of doping in Mn-Zn ferrites

We investigate the effect of different doping schemes on the broadband magnetic losses and their temperature dependence in Mn-Zn ferrites. CaO, Nb2O5, ZrO2, and SiO2 are added with increasing proportions to TiO2-doped prefired powders and, after sintering at either 1275 °C or 1300 °C, the obtained ring samples are tested versus frequency f (DC-1 GHz) and peak polarization Jp (2 mT – 200 mT) up to T = 160 °C. Appropriately enhanced impurity contents are shown to induce further decrease of the energy loss in materials already prepared for best performance at high temperatures (140 – 160 °C). This behavior can be hardly ascribed to the impurity-related increase of the electrical resistivity brough about by extra-doping, being it rather connected to a corresponding monotonical decrease of the effective magnetic anisotropy < Keff > with T. The decreasing anisotropy makes the balance between the contributions of domain wall (dw) displacements and reversible rotations to the magnetization process evolving in favor of the latter. The energy loss correspondingly develops with frequency and peak polarization in a complex fashion, according to the specific dissipative mechanisms sustained by the spins precessing either inside the moving walls or in the bulk. A dividing line in the (Jp − f) plane is identified, which separates dominant dw- and rotation-generated losses. It moves downward (i.e. lower f) with increasing temperature, the higher T the lower the frequency at which the rotations, theoretically assessed via the Landau-Lifshitz equation, supersede the domain wall contribution. Once accomplished, however, the transition to rotations can lead, according to the theoretical model, to higher losses when moving to higher temperatures. Following the experimental trend of the complex resistivity versus frequency at different T values, the calculations and the experiments show that eddy currents start to contribute to the energy loss, in the 5 mm thick ring samples, around a few MHz, accounting for about 50 % of measured loss beyond some 50 MHz. The chief dissipative process at applicative frequencies and induction values is therefore identified with spin damping, to which the generalized loss decomposition method can be applied.

Unified framework of forced magnetic reconnection and Alfvén resonance

A unified linear theory that includes forced reconnection as a particular case of Alfvén resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency ω0. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfvén resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfvén resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times t≫S1/3, when the forcing frequency of the boundary perturbation is ω0≪S−1/3, allowing the coupling of the Alfvén resonances across the neutral line with the reconnecting mode, as originally suggested in Uberoi and Zweibel, (1999). Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies ω0≫S−3/5.

Design, Simulation and Analysis of Circular and Elliptical Antennas for 5G Applications

This research examines the design and simulation of both circular and elliptical microstrip antennas tailored for use in 5G technology, utilizing Ansoft HFSS software. The study assesses these antennas on parameters such as bandwidth, gain, and radiation patterns, aiming to meet the complex frequency demands of 5G networks. The findings suggest that circular antennas provide consistent omnidirectional coverage, whereas elliptical antennas excel in targeted coverage, essential for effective 5G communications. Moreover, elliptical antennas demonstrate significant benefits in point-to-point communications through adjustable radiation patterns. The paper offers insights into refining these antenna designs to cater to diverse 5G networking needs and proposes specific design changes to enhance their performance.

Vehicle detection in varied weather conditions using enhanced deep YOLO with complex wavelet

Traffic congestion is prevalent in many major and medium-sized cities throughout different countries in contemporary society. In traffic images, various multi-sized vehicles are tightly clustered together and obstructed from one another. Identifying vehicles in such instances is crucial for urban traffic surveillance, safety monitoring, and legal concerns but it also presents major challenges. The remarkable detection accuracy and efficiency of deep learning-based systems have led to their recent and extensive use in vehicle identification. There are significant advanced YOLO models with different backbone architectures and frameworks developed for vehicle detection. Yet, the performance of YOLO variants are facing the challenges of handling false detection against occluded and densely sophisticated scenarios. The proposed model is developed to address such types of limitations, for example; dynamic illumination, noisy images, and scale sensitivity to improve the vehicle detection rate in different traffic scenarios and varying weather conditions. The proposed study employs an improved YOLOv4 to identify moving vehicles in different lighting conditions including daylight, cloudy, rainy, and night. For hybridization, three techniques are utilized such as the Multiscale Retinex, Dual tree complex wavelet transform (DTCWT), and Pulse Coupled Neural Networks (PCNN). The DTCWT is employed for multiscale decomposition and to denoise the complex high frequency subband information, then the denoised subbands are reconstructed into a denoised image. The Multiscale retinex is utilized to reduce the halo artifacts on high-contrast edges and maintain the balance with dynamic range compression and color reproduction. The synchronizing pulse burst property of PCNN is used to detect the isolated noisy pixels and modify the detected noisy pixels. From the results it is worth noting that the developed model surpasses state-of-the-art methods in sunny, night, cloudy, and rainy modes. The proposed method using the DTCWT technique can detect the vehicles with mAP of 91.09% and 35FPS.