Nonlinear Characteristics Research Articles

An Improved Spatiotemporal Time Series Modelling Procedure with Application to Forecasting of Solar Radiation

The demand for energy and associated services to meet sustainable agricultural and economic growth and improve human health and lifestyle is increasing day by day. Hence, there is a need for systematic and scientific prediction of solar and other renewable sources of energy to meet these requirements. The main purpose of this study is to propose a hybrid Space-Time Autoregressive Moving Average Artificial Neural Network (STARMA-ANN) model for the precise and accurate forecasting of solar radiation for better planning and policy making. This approach has been implemented at seven geographical locations of Bihar in India. Spatial weight matrices have been used to describe all seven geographical locations and incorporated into the STARMA model to reflect the spatial and temporal correlation. To deal with nonlinear dynamics in the spatiotemporal data, ANN technique has been applied on residuals of the fitted STARMA model. The results have demonstrated that the proposed hybrid model performs better prediction accuracy than using conventional STARMA model, especially for spatiotemporal data with nonlinear characteristics of solar radiation.

A novel grey seasonal model with time power for energy prediction

The fluctuation of seasonal time series has attracted considerable attention. However, the complexity of socio-economic development and the variability of influencing factors make accurate predictions of seasonal time series more difficult. A new discrete grey seasonal model, namely DGSTPM(1,1), is established, which employs the time power term based on the cultural algorithm to effectively deal with the time sequences characterized by nonlinear tendency and periodic fluctuations. Firstly, the operating mechanism of the DGSTPM(1,1) model is expounded by combining the time power item with the traditional grey seasonal model to enhance the forecasting capability. Then, the optimal time power index of the model can be determined by incorporating the cultural algorithm. Subsequently, several properties are thoroughly discussed to illustrate the superiority and uniformity of the new model. Finally, two energy-related cases with different data features and sample sizes are applied to identify the efficacy and robustness of the DGSTPM(1,1) model, referring to monthly crude oil production in the United States and quarterly coke production in China. Based on the various error criteria, SPA and DM tests, the results indicate that the DGSTPM(1,1) outperforms its competitors both in simulation and prediction phases, including DGSTM(1,1), SGM(1,1), SDTGM, FTGM, SARIMA, LSSVM, BPNN, and LSTM models. Meanwhile, the new model can effectively address seasonal time series with nonlinear characteristics owing to its dynamic time power item with the support of the cultural algorithm.

RIME-CNN-BiLSTM: A novel optimized hybrid enhanced model for significant wave height prediction in the Gulf of Mexico

Accurate prediction of SWH in the ocean is critical to the development of ocean energy technologies. However, existing forecasting models have limitations in accuracy and reliability, which directly affect the efficiency of ocean energy utilization. To address this problem, this paper proposes a new ocean SWH prediction model, RIME-CNN-BiLSTM, for predicting 1, 6, 12, and 24 h SWH at three buoy observing stations in the Gulf of Mexico. The model combines the RIME algorithm, CNN, and BiLSTM to comprehensively capture multiple parameters that affect wave heights, such as sea breeze, waves, barometric pressure, and temperature. The parameters of the CNN-BiLSTM model are optimized by the RIME algorithm, which significantly improves the prediction accuracy and generalization ability. Compared with the traditional model, RIME-CNN-BiLSTM captures the nonlinear features more accurately, has better prediction ability for outliers, and shows stronger generalization performance in different sea areas of the Gulf of Mexico. In terms of predicting the wave height in the next 24 h, the improvements are 7.065%, 3.646% and 5.186%, respectively. The results show that the RIME-CNN-BiLSTM model performs well in all prediction time periods, significantly outperforms other benchmark models, and is able to accurately capture nonlinear features and effectively predict outliers.

Nonlinear vibration characteristics of rotor-bearing system with disc-shaft insufficient interference and flexible coupling misalignment fault

Abstract For the traditional rotor system, the looseness fault caused by disc-shaft insufficient interference is always ignored. Aimed at the disc-shaft looseness caused by insufficient interference, a novel dynamic model of rotor-bearing system in the presence of coupling misalignment is established in this paper to make an investigation on the fault characteristics of disc-shaft looseness fault. Due to the nonlinearity of contact model between disc-shaft, the iterative solving of kinetic equations can be obtained by the combination of Newmark-β and Newton-Raphson methods. The vibration characteristics of the rotor-bearing system with and without the disc-shaft looseness caused by insufficient interference are compared and analyzed. The comparison results show that the slight collision between disc-shaft can be caused in the disc-shaft early looseness fault, and the beat vibration of system is appeared when the disc-shaft looseness become severe. Considering the effect of coupling misalignment, the vibration responses of system under different coupling misalignment are further discussed and parallel misalignment is proved to have a significant effect on the disc-shaft looseness. It is expected that the research results provide a useful reference for the identification and diagnosis of the looseness fault caused by disc-shaft insufficient interference.

Nonlinear friction dynamics of water-lubricated bearings under transient shocks considering cavitation and turbulence effects

This study proposes a transient elastohydrodynamic mixed lubrication (EHML) model for water-lubricated bearings (WLBs) that incorporates cavitation and turbulence effects to evaluate the nonlinear friction dynamic performance under transient shock loads. The generalized average Reynolds equation is discretized using the control volume technique (CVM), and the constrained system is solved using the Fischer-Burmeister-Newton-Schur (FBNS) method. The validity of the model is verified by a comparison of experimental data from published literature. On this basis, the effects of cavitation, turbulence, shock load amplitude, direction, time, and rotational speed on WLB nonlinear friction dynamics characteristics are investigated. The results show that cavitation induces hydrodynamic loss under transient shock conditions, significantly increases contact time and load, and exacerbates the hydrodynamic instability phenomenon. In contrast, the turbulence effect effectively reduces frictional contact. The stability of WLBs under transient shock conditions is closely related to the load offset angle. Reducing the load offset angle improves the anti-shock stability of the bearings. Nevertheless, an increase in the amplitude and duration of the shock load may result in a deterioration of the frictional contact behavior. Increasing the rotational speed appropriately favors accelerating the lubrication regime transition and improving WLB’s anti-shock stability. This study provides a reference for enhancing WLB anti-shock performance and optimizing structural design.

Ion temperature gradient modes modulational stability with kappa-distribution

We investigated the modulational stability and instability of the ion temperature gradient (ITG) mode in electron-ion plasma. Ions are dynamic species, whereas electrons follow a Kappa distribution. We used the reduction perturbation approach to determine the linear dispersion relation for the fluid under consideration. The nonlinear Schrodinger equation describes nonlinear features such as nonlinear modulational stability or instability in the ITG mode. The product of dissipation and nonlinear coefficients, known as LM, contains both modulational stability and instability in the ion temperature gradient mode. Theoretical results are expanded numerically, showing the influence of various plasma parameters on modulational stability and instability, particularly the superthermality coefficient κ e . The current observations may be extended to space and laboratory plasma for modification.

High-dimensional nonlinear flutter suppression of variable thickness porous sandwich conical shells based on nonlinear energy sink

Nonlinear energy sink (NES) is widely applied in engineering field due to the advantages of light weight, high robustness, unidirectional energy transfer, rapid and broadband vibration isolation. In this paper, nonlinear energy sink is utilized to suppress vibration of the variable thickness porous sandwich conical shells for the first time, and the high-dimensional nonlinear flutter suppression characteristics of the system of simply supported variable stiffness truncated porous sandwich conical shell coupled NES under aerodynamic force and thermal stress are investigated. By applying the first-order shear deformation theory (FSDT), Hamilton's principle and Galerkin technique, the high-dimensional nonlinear ordinary differential flutter suppression equations of the system appended with NES are established. The accuracy of the theoretical approach is ensured by the comparison of frequency results, while the NES dissipated kinetic energy ratio and the comparison of NES performance with other suppression systems are presented to prove the effectiveness of NES on nonlinear flutter suppression. The time history diagrams and limit cycle oscillation (LCO) amplitude curves, which reflect the high-dimensional nonlinear flutter suppression effect of NES, are obtained by employing the Runge-Kutta method. The effects of aerodynamic pressure, the parameters and positions of single NES, and the positions of parallel NES and series NES on the high-dimensional nonlinear flutter suppression characteristics of the system attached with NES are discussed in depth. Finally, the optimal high-dimensional nonlinear flutter suppression scheme is arrived.

Investigation of Nonlinear Optical Properties of NiO Nanoparticles using the Z-Scan Technique

In this research, linear and nonlinear optical properties of NiO nanoparticles (NPs) dissolved in ethanol were investigated. Linear optical characteristics of NiO NPs were studied using a UV-Vis spectrophotometer. The linear absorption coefficient (α0) was 0.88 and 0.57 cm-1 at 405 and 532 nm wavelengths, respectively. The band gap energy rose from 3.56 eV for a sample with a 10-7 g/ml concentration to 3.92 eV for the 10-3 g/ml concentration sample. Using the Z-scan technique, the nonlinear optical characteristics of the NPs were investigated. Two continuous wave laser diodes with 405 and 532 nm wavelengths and different powers were used. The Z-scan system with a closed aperture revealed that NiO NPs have a negative n2 (self-defocusing effect) at various laser powers. n2 increases as the power of the laser increases. The value of n2 was found to be 0.51×10-4 cm2/mW at a wavelength of 405 nm and a power of 0.33 mW. It improved as the laser power increased, reaching a maximum of 0.64×10-4 cm2/mW at a laser power of 1.51 mW. For the laser with a wavelength of 532 nm, the n2 value was 0.27×10-4 cm2/mW for a laser power of 1.01 mW. This value increased to 0.76×10-4 cm2/mW when the laser power increased to 6.2 mW. As measured by the Z-scan system with an open aperture, NiO NPs have a nonlinear absorption coefficient and display a two-photon absorption behavior.

Optimal Battery Storage Configuration for High-Proportion Renewable Power Systems Considering Minimum Inertia Requirements

With the continuous development of renewable energy worldwide, the issue of frequency stability in power systems has become increasingly serious. Enhancing the inertia level of power systems by configuring battery storage to provide virtual inertia has garnered significant research attention in academia. However, addressing the non-linear characteristics of frequency stability constraints, which complicate model solving, and managing the uncertainties associated with renewable energy and load, are the main challenges in planning energy storage for high-proportion renewable power systems. In this context, this paper proposes a battery storage configuration model for high-proportion renewable power systems that considers minimum inertia requirements and the uncertainties of wind and solar power. First, frequency stability constraints are transformed into minimum inertia constraints, primarily considering the rate of change of frequency (ROCOF) and nadir frequency (NF) indicators during the transformation process. Second, using historical wind and solar data, a time-series probability scenario set is constructed through clustering methods to model the uncertainties of wind and solar power. A stochastic optimization method is then adopted to establish a mixed-integer linear programming (MILP) model for the battery storage configuration of high-proportion renewable power systems, considering minimum inertia requirements and wind-solar uncertainties. Finally, through a modified IEEE-39 bus system, it was verified that the proposed method is more economical in addressing frequency stability issues in power systems with a high proportion of renewable energy compared to traditional scheduling methods.

Perceived Trajectories of Cyclic Sound Movement

Binaural beats are a phenomenon that occurs during dichotic stimulation due to binaural integration. It takes the form of cyclic movement of the sound image in the listener’s acoustic space when the beat frequency range is below 3 Hz. Our subjects used the inserted earphones to listen to the stimuli that created a sense of sound movement due to changes in the interaural time difference (ITD). We used three types of dichotic stimuli which simulated smooth azimuthal cyclic movement and cyclic abrupt shifts. The ITD changes determined central or lateral positions of movement trajectories. The results confirm that both types of movement created the effect of binaural beats. The range of beats depended on the spatial position of the trajectory: in the frontal sector of acoustic space, the range of beats was greater than on the left or right. The perceived trajectories of smooth motion were shorter than the trajectories of abrupt shift. The influence of spatial position on the perceived trajectory length is interpreted from the standpoint of nonlinear features of lateralization. It is suggested that the effect of ITD pattern on the perceived trajectory length is mediated by temporal integration mechanisms of binaural hearing.

Interlayer engineered bilayered V₂O₅ NPs as saturable absorbers for infrared ultrashort pulse generation

Interlayer engineering offers a promising approach to modifying the structure of layered vanadium-based oxides, enhancing their saturable absorption effect and making them a desirable choice for developing infrared wavelength-range photonics devices. This experimental work synthesizes interlayer vanadium pentoxide (V2O5) using hydrothermal techniques to produce an excellent saturable absorber (SA). The interlayer engineering strategy enhances strong saturable absorption and self-defocusing effects in V2O5-based SA, enabling the generation of ultrashort pulses in the infrared region. Their superior nonlinear optical characteristics are demonstrated by a modulation depth of 13.9 % and saturation intensity of 0.42 GW cm−1, respectively. By utilizing a transmission coupling fiber-based V2O5-SA inside an Er-doped fiber laser cavity, a passively Q-switched (PQS) laser with a narrow pulse width of 2.78 μs and signal-to-noise ratio (SNR) ∼50 dB is realized for the first time. Furthermore, we explore a V2O5 NPs-SA long-term stability and high damage threshold. The results not only offer additional proof of the capable potential of interlayer V2O5 as a photo-bleaching absorber for realizing pulsed lasers in the NIR band but also cover the method for advancing their probable applications in optoelectronic devices.

A Study of Friction Nonlinearity and Compensation for Turntable Servo Systems

In view of the worse dynamic performance and steady-state accuracy caused by nonlinear friction in turntable servo systems, challenges are posed in precise positioning tasks. However, most of the existing research ignores the effect of friction on system performance. Therefore, it is of great significance to analyze the nonlinear characteristics of the transmission mechanism and study compensation strategies for improving the control quality of non-direct drive turntable servo systems. Therefore, an improved active disturbance rejection control (ADRC) based on state feedback compensation is proposed in this paper to optimize the accuracy of the turntable servo system and improve the robustness of the system under nonlinear friction conditions. Firstly, friction is modeled and analyzed through offline identification, which is the basis for nonlinear friction compensation. Subsequently, the two methods of friction compensation are compared. Since feedforward compensation is prone to under-compensation and over-compensation, it is highly dependent on the parameters, while the traditional ADRC compensation method has poor dynamic performance under gap conditions. Therefore, the advantages of ADRC and state feedback are combined together to reduce the steady-state error and optimize the control performance of the system. Lastly, the effectiveness of the proposed compensation method is verified and compared through simulations and experiments. The method is able to comprehensively compensate the gap and friction nonlinearities, and the experimental steady-state error is reduced from 0.55° to 1/3 (0.19°), which improves the load-side positioning accuracy. Finally, a conclusion can be drawn that the new compensation method can improve the parameter adjustability, speed estimation precision, and system robustness.

An enhanced maximum power point tracking and voltage control for proton exchange membrane fuel cell using predictive model control techniques

Proton Exchange Membrane Fuel Cells serve as sustainable devices for converting renewable energy sources into electricity, offering advantages such as rapid startup, high power density, and operation at low temperatures. They are highly efficient and environmentally friendly energy sources, yet their non-linear output characteristics under variable conditions present challenges in maximizing power output. Furthermore, they generates direct current, while many electrical devices rely on alternating current. This research addresses the necessity of enhancing the performance and efficiency through the development of an advanced maximum power point tracking technique and voltage control strategy. A modified finite-control-set model predictive control technique is proposed for both maximum power point tracking and voltage control. Specifically, a finite-control-set model predictive control technique approach is employed to modulate the switching signal for both the DC-DC boost converter and the DC-AC inverter. The DC-DC boost converter step up the fuel cell output voltage to the desired level, ensuring it reaches the maximum power point, and a DC-AC inverter to convert the direct current voltage to a pure sinusoidal alternating waveform. The investigation demonstrates the effectiveness of the proposed method in achieving its objectives. The proposed maximum power point tracking technique accuracy achieved the maximum power with a rate of 97 % with excellent respond time within 7 ms. For alternating current power, only less than 1.5 % of total harmonic distortion is recorded. The study evaluates the control scheme under robust operating conditions, demonstrating its effectiveness in optimizing PEMFC output and providing high-quality AC voltage.

Depinning of charge density waves of different dimensionalities in 1T-TiSe2 and NbSe3

Nonlinear transport behavior is one of the signatures of the formation of electronic crystals such as charge density wave (CDW), as it provides evidence for their collective motion. Such experimental evidence has been widely reported in quasi-one-dimensional (1D) materials but is rarely studied in 2D systems. Only a few studies on the RTe3materials have been previsouly reported. Here we report for the first time the observation of CDW depinning and sliding in the layered 1T-TiSe2compound, based on the observation of (1) nonlinear voltage-current characteristics and (2) the electrical noise, which are associated with the CDW depinning and sliding process. Similar measurements are also conducted on quasi-1D system NbSe3. The depinning behavior of the CDWs with different dimensionalities in these two systems are compared. It is found that the threshold electric field (ET) increases linearly with decreasing temperature for the 2D case, consistent with previous results on RTe3, while it demonstrated an activated behavior in 1D, as expected within the weak-pinning Fukuyama-Lee-Rice framework. Such a distinction of the threshold behavior in CDW systems of different dimensions therefore indicates a possible strong pinning picture in higher-dimensional CDW systems in general.ETis found to be much higher in 1T-TiSe2, consistent with a strong pinning picture, and could account for the scarcity of the depinning study in these 2D systems. Our results thus pave the way for a unified understanding of the CDW collective motion in different dimensionalities.

Modeling and compensation of a hollow XY stage based on hybrid reluctance actuators

In the field of beam pointing and optoelectronic imaging, there is a growing demand for control mechanisms that offer large stroke, and high bandwidth. These are precisely the characteristics of hybrid reluctance actuator, which therefore is increasingly being used in XY stage to replace piezo-actuator and voice coil motor. This study presents a hollow XY stage utilizing hybrid resistance actuators, aiming to adapt to optical applications with inherent nonlinearity and biaxial coupling, which are further modeled and compensated to mitigate their impacts. Firstly, the basic composition and working principle of the hollow XY stage are described, and the impact of its nonlinearity and biaxial coupling characteristics is elucidated. Secondly, the sources of nonlinearity and biaxial coupling are analyzed, and an analytical model of hybrid reluctance actuators is established. The magnetic leakage coefficient of the model is determined, and the accuracy of the model is verified by Finite Element Method (FEM) and experiment, demonstrating consistency with the analytical model's results. Furthermore, based on the nonlinear and biaxial coupling model, a compensator based on feedback linearization method is established, and verified through experiment. The results show that this method has a significant suppression effect on nonlinear and biaxial coupling, and the tracking error and cross-talk is obviously reduced, which proves the effectiveness of this compensation method.

Nonlinear guided wave mixing in weld joints for detection of material nonlinearity

The remarkable sensitivity of ultrasonic waves to detect the early stages of material degradation stems from their inherent nonlinear nature. However, distinguishing the nonlinearity induced by the measurement system from that of the weak materials remains a persistent challenge in second harmonic generation methods. Ultrasonic wave mixing has emerged as a feasible solution for isolating nonlinearities originating from the measurement system. While bulk waves, surface waves, and guided waves have undergone extensive study in wave mixing, the potential of feature-guided wave (FGW) mixing remains largely unexplored. This paper investigates the mutual interaction of FGWs to generate second-order mixed harmonic waves, focusing specifically on weld joints. Acoustic energy trapped along structural features such as weld joints exhibits reduced decay compared to uniform plates, making them ideal for nonlinear characterization. We investigate the effectiveness of FGW mixing for characterizing material nonlinearities in welded joints, utilizing phase velocity matching and resonance criteria to enhance the generation of mixed harmonic components. Through three-dimensional numerical simulations and experimental tests, we showcase the generation of mixed harmonics induced by the mixing of FGWs. Our findings underscore the potential of FGW mixing as a novel approach for enhancing nonlinear-based damage detection techniques in welded joints.

A Review of Model Predictive Control for the Municipal Solid Waste Incineration Process

Municipal solid waste incineration (MSWI) is essential for tackling urban environmental challenges and facilitating renewable energy recycling. The MSWI process has characteristics of multiple variables, strong coupling, and complex nonlinearity, requiring advanced process control (APC) technology. Although there have been several reviews on the modeling and control of the MSWI process, there is a lack of focus on model predictive control (MPC), a widely used APC technology. This article aims to comprehensively review MPC strategies in the MSWI process. First, it describes MSWI process technology in detail, examining control issues and objectives to highlight the complexity and challenges in controller design while providing an overview of MPC methods and their benefits. Second, it reviews incinerator modeling for control, including traditional modeling techniques and machine learning technologies such as fuzzy neural networks. Third, it reviews the controllers used for MSWI process, emphasizing the advantages of MPC over existing control methods. Fourth, it discusses the current status of MPC design and online updates, covering the need for an accurate dynamic predictive model and objective function and the online updates components such as predictive modeling, rolling optimization, and feedback correction. Finally, the study concludes with a summary of the findings.

Effect of relative phase of loose tie rods on nonlinear dynamic behavior of rod-fastening rotor-bearing-seal system

Loosening of multiple tie rods in a circumferential rod-fastening rotor caused by thermal deformation and centrifugal loads is very common in engineering. The relative position of loose tie rods in the circumferential direction will also have an important impact on rotor dynamics. The relevant research has not been done yet. In this paper, a contact model of the rough machined surface is firstly established by combining the probability functions describing rough surfaces and fractal contact theory of asperities, then the contact stiffness model between disks is established based on the contact model. Finally, the dynamic model of the circumferential rod-fastening rotor-bearing-seal system is established and solved. The effect of relative phase of loose tie rods on the nonlinear dynamic characteristics of rod-fastening rotor-bearing-sealing system is studied. It can be concluded that relative phase of the loose tie rod has an important influence on the frequency, bifurcation, and periodic motion of the rotor system. At lower speed, the anisotropy of contact stiffness caused by loose tie rods has little effect on the rotor trajectory, while the generalized bending moment has a greater influence on dynamics of the system. At higher speed, the anisotropy of contact stiffness has a great influence on the axis rail of the rod-fastening rotor.

Fuzzy Modelling Algorithms and Parallel Distributed Compensation for Coupled Electromechanical Systems

Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system’s components, thermal effects, mechanical vibrations, electrical noise, and the dynamic and transient impacts of electrical loads. In this study, we introduce a fuzzy modelling identification approach utilizing the Takagi–Sugeno (T–S) structure, wherein model and control parameters are optimized. This methodology circumvents the need for deriving a mathematical model through energy balance considerations involving thermodynamics and the non-linear representation of the electric generator. Initially, a non-linear mathematical model for the electrical power system is obtained through the fuzzy c-means algorithm, which handles both premises and consequents in state space, utilizing input–output experimental data. Subsequently, the Particle Swarm Algorithm (PSO) is employed for optimizing the fuzzy parameter m of the c-means algorithm during the modelling phase. Additionally, in the design of the Parallel Distributed Compensation Controller (PDC), the optimization of parameters pertaining to the poles of the closed-loop response is conducted also by using the PSO method. Ultimately, numerical simulations are conducted, adjusting the power consumption of an inductive load.

Relationship between the induced voltage of a rotor bar and the rotation characteristics of a high-temperature superconducting induction motor

Although high-temperature superconducting induction motors have a simple structure, they are distinguished by their high efficiency and high power density. However, an accurate theoretical model that defines the primary electrical characteristics controlling the motor has not been established because of the nonlinear characteristics of high-temperature superconducting squirrel-cage rotor winding. As part of establishing such a model, an experiment was conducted to analyze the relationship between the induced voltage of the rotor bar in a high-temperature superconducting squirrel-cage rotor winding and stator-side quantities (voltage and transport current), as well as its rotation characteristics. A subject was a 1.5 kW class induction motor using Bi–Sr–Ca–Cu–O high-temperature superconducting rotor bars and the experiment was performed at a temperature and a frequency of 77 K and 60 Hz, respectively. The induced voltages of the rotor bars were measured by applying a rotating magnetic field and exhibited a distorted waveform characterized by a third-order harmonic in a magnetic flux flow state. Despite the distorted voltage waveform of the rotor bar, the stator transport current responsible for driving the induction motor remained unaffected and the motor initiated rotation in a slip rotation mode. From the above results, it was experimentally clarified that a stator voltage exceeding the critical current of the rotor bar must be applied when starting the induction motor. It was also shown that the rotor bar can be regarded as a constant resistance for a constant effective value of the stator current when transitioning the motor into a slip rotation state.