Nonlinear Coupling Processes Research Articles

Neural network model predictive control of core power of Qinshan nuclear power plant based on reinforcement learning

The power change of Pressurized water reactors (PWRs) is a highly complex nonlinear coupling process, which requires the power controller to have a high nonlinear control capability. Since the traditional model predictive control (MPC) algorithm has the problems of insufficient robustness and adaptivity, this study proposes a neural network-based neural network model predictive control method based on model predictive control and optimizes its control parameters in real time by using the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm. The designed control method is validated on the simulation model of the Qinshan nuclear power plant (NPP). Simulation results show that the proposed control method can realize effective control of power under a variety of power changing conditions and dynamic adjustment of control parameters.

What are the dominant drivers and optimal thresholds for a healthy ecosystem in the Yellow River Basin, China? from a perspective of nonlinear nexus

Identifying the dominant factors influencing ecosystem health and their optimal thresholds is essential for the management and restoration of ecosystems. Most of the works, however, have less detected the importance level of individual factors, especially their changes over time and scale, and rarely determined their threshold effects on ecosystem health (EH), which seriously hinders the formulation of targeted policies for sustainable ecosystem management. To address these research gaps, we present an innovative visualization approach to reveal importance changes in natural and anthropogenic variables and their nonlinear coupling process with EH in the China’s Yellow River Basin (YRB) in the last two decades. Results show that (i) Although the EH in the YRB has improved slightly in the past 20 years, it is still not optimistic and shows distinct spatial heterogeneity. (ii) The impact of human activities on the ecosystem health of the YRB has increased and increasingly plays a decisive role, while that of the natural aspect has decreased recently. Specifically, environmental factors (slope, NDVI, and annual temperature) are the dominant factors affecting the upstream EH. Midstream EH is significantly affected by the synergistic effect of natural and anthropogenic factors, but the importance of the proportion of built-up land is intensified (ranked from 8th to 4th). Anthropogenic factors exert the greatest influence on downstream EH variation, especially for population density whose importance order rising from 7th to 2nd. (iii) By illustrating the nonlinear response curves of EH at multi-scale, the tipping point caused ecosystem deterioration in the YRB is explored and the optimal thresholds of leading factors oriented towards the most effective ecosystem conservation goal are obtained. These results help precisely identify the current health status of YRB's ecosystem, as well as providing a valuable reference for moderate restoration standards and sustainable ecosystem management.

Dynamics of dissipative structures in coherently-driven Kerr cavities with a parabolic potential

By means of a modified Lugiato–Lefever equation model, we investigate the nonlinear dynamics of dissipative wave structures in coherently-driven Kerr cavities with a parabolic potential. This potential stabilizes the system dynamics, leading to the generation of robust dissipative solitons in the positive detuning regime, and of higher-order solitons in the negative detuning regime. In order to understand the underlying mechanisms which are responsible for these high-order states, we decompose the field on the basis of linear eigenmodes of the system. This permits to investigate the resulting nonlinear mode coupling processes. By increasing the external pumping, one observes the emergence of high-order breathers and chaoticons. Our modal content analysis reveals that breathers are dominated by modes of corresponding orders, while chaoticons exhibit proper chaotic dynamics. We characterize the evolution of dissipative structures by using bifurcation diagrams, and confirm their stability by combining linear stability analysis results with numerical simulations. Finally, we draw phase diagrams that summarize the complex dynamics landscape, obtained by varying the pump, the detuning, and the strength of the potential.

Bifurcation of coherent vortex flow in a magnetic island through nonlinear parity instability

The topology of the vortex flow associated with the magnetic island plays a significant role in modulating the turbulent transport near the magnetic island. In this paper, self-consistent nonlinear simulations of multi-scale interactions among large scale tearing mode, vortex flow, and small scale ion temperature-gradient (ITG) mode are numerically investigated based on the five-field Landau-fluid model. We found that the coherent vortex flow in a magnetic island has different parities in the nonlinear quasi-steady state, and this can be described by a theoretical framework—nonlinear parity instability. In the ITG stable case, the structure of the vortex flow bifurcates from tearing parity to twisting parity, which is characterized by modulational parity instability, modeled by a four-wave nonlinear coupling process. In the ITG unstable case, the vortex flow stays in tearing parity without parity bifurcation, and the energy is transferred from the twisting parity modes to the tearing parity modes. The impact of the parity instability on the magnetic island width is discussed as well.

What are the dominant factors and optimal driving threshold for the synergy and tradeoff between ecosystem services, from a nonlinear coupling perspective?

Exploring the dominant impact factors and optimal driving threshold of the synergic and trade-off relationship between ecosystem services (ESR) is conducive to the scientific management of the ecosystem. Previous studies seldom take ESR as dependent variables and are primarily based on linear regression models, which is difficult to reflect the real nonlinear ecological process. Based on the spatial mapping for 15 pairs of binary ESR between 6 typical ESs in Fujian Province, this study introduced “glass box” (interpretable and visual) machine learning models to construct a generalizable ESR driving mechanism exploration method system of “ESR spatialization - nonlinear correlation derivation”. It visually expounds the nonlinear coupling process between ESR and " natural-socio-economic " variables, and based on this, the dominant factors affecting ESR and their optimal driving threshold interval for the maximized synergy between ESs were determined. The results show that (i) the climate and human traffic activities have the most significant effect on the ESR among the “natural-socio economic” factors. Annual total precipitation, annual sunshine radiation, average annual temperature, distance from railway, and GDP density are the dominant factors affecting the ESR in the sample area. (ii) The correlation between ESR and driving factors is nonlinear. By superimposing the nonlinear response curves of 15 pairs of ESR, the optimal threshold interval of the dominant factor under the guidance of comprehensive synergy maximization in the study area is obtained. (iii) In the comparison of three machine learning models and a linear regression model, the XGBoost model has the best fitting effect, and the machine learning models are all superior to the linear model. The methods and ideas of this study have strong generalization and application and can provide references for research in other regions and scales.

Multi-objective optimization design of TRISO-based fully ceramic microencapsulated fuel

Fully Ceramic Microencapsulated (FCM) fuel is a new type of material in nuclear energy field. It has become a promising accident tolerant fuel (ATF) candidate due to its advantages of high radiation stability, high fission product containment capacity and excellent thermo-mechanical performance. During operation, the temperature, stress, deformation and other key parameters will change significantly, which directly affect the safety of nuclear reactor. Therefore, it is necessary to carry out a multi-physics fully-coupled analysis suitable for the multi-scale, multi-component, multi-phase and nonlinear coupling processes in the reactor, so as to sort out the influences of material properties, radiation behavior, thermo-mechanical performance from numerous influencing factors. In this paper, based on the irradiation-thermo-mechanical coupling method, the performance of TRISO-based FCM fuel under irradiation conditions was analyzed, key thermo-mechanical parameters and other influencing factors of the fuel were obtained, failure behavior of the fuel element was evaluated. On this basis, the theoretical and numerical model of multi-objective optimization method were established, the optimum parameters including material properties, fuel geometry and particle arrangement were found by optimization method. The optimization results showed that the multi-objective optimization results could provide multiple Pareto optimal solutions for the FCM fuel. Specifically, when the TRISO particle spacing is 200 µm and 150 µm, the objective function difference between the optimal heat transfer solutions is only about 1.7%, meanwhile the mechanical properties vary significantly (the difference between the objective functions of the optimal solutions is about 12.4% ∼26.5%), indicating the response of stress is more sensitive than temperature. When the TRISO particles are tightly packed (particle spacing less than 100 µm), the difference of objective function between the optimal solutions is less than 5%, illustrating the optimization has limited improvement on the thermo-mechanical performance of the fuel, namely the optimization space is limited.

Real-Time Control of Gas Supply System for a PEMFC Cold-Start Based on the MADDPG Algorithm

During the cold-start process of a PEMFC, the supply of air and hydrogen in the gas supply system has a great influence on the cold-start performance. The cold-start of a PEMFC is a complex nonlinear coupling process, and the traditional control strategy is not sensitive to the real-time characteristics of the system. Inspired by the strong perception and decision-making abilities of deep reinforcement learning, this paper proposes a cold-start control strategy for a gas supply system based on the MADDPG algorithm, and designs an air supply controller and a hydrogen supply controller based on this algorithm. The proposed strategy can optimize the control parameters of the gas supply system in real time according to the temperature rise rate of the stack during the cold-start process, the fluctuation of the OER, and the voltage output characteristics. After the strategy is trained offline according to the designed reward function, the detailed in-loop simulation experiment results are given and compared with the traditional control strategy for the gas supply system. From the results, it can be seen that the proposed MADDPG control strategy has a more effective coordination control effect.

Super-resolution acoustic imaging

This work reports a super-resolution acoustic imaging method that inverses source distribution, strength, and structure in three-dimensional space. The nonlinear coupling process between a low-frequency sound field and a high-frequency plane wave is endowed to break the resolution limit. The reconstructed results for different source strengths and frequencies demonstrate the capability of the proposed method. The results show that the proposed method is very suitable for low-frequency source imaging, which could strengthen the super-resolution analysis capability of acoustic imaging tests and, consequently, lead to deepened physical insights into various propulsion systems in underwater and aerospace systems.

Nonlinear Identification and Control of Laser Welding Based on RBF Neural Networks

A laser beam is a heat source with a high energy density; this technology has been rapidly developed and applied in the field of welding owing to its potential advantages, and supplements traditional welding techniques. An in-depth analysis of its operating process could establish a good foundation for its application in China. It is widely understood that the welding process is a highly nonlinear and multi-variable coupling process; it comprises a significant number of complex processes with random uncertain factors. Because of their nonlinear mapping and self-learning characteristics, artificial neural networks (ANNs) have certain advantages in comparison to traditional methods in the field of welding. Laser welding is a nonlinear dynamic process; these processes still pose a major challenge in the field of control. Therefore, establishing a stable model is a prerequisite for achieving accurate control. In this study, the identification and control of radial basis function neural networks in laser welding processes and self-tuning PID control methods are proposed to improve weld quality. Using a MATLAB simulation, it is shown that the proposed method can obtain a good description of the level of nonlinear dynamic control, and that the algorithm identification accuracy is high, practical, and effective. Using this method, the weld width quickly reaches the expected value and the system remains stable, with good robustness. Further, it ensures the stability and dynamic performance of the welding process and improves weld quality.

Dynamic Modeling and Control Law Design of a Fuel-electric Hybrid Multi-rotor UAV

In this paper, the design of control law for a new concept fuel-electric hybrid multi-rotor UAV with lift/attitude control separation is investigated. The remarkable feature of the UAV is that it has a large proportion of fuel weight. Firstly, based on the quasi-coordinate Lagrangian equation and sloshing equivalent model using the multi-mass-spring analogy, the non-linear dynamic model of the UAV considering the fuel slosh dynamics is established. Compared with the existing multi-rotor modeling method, it is more intuitive and accurate to describe the non-linear coupling process of sloshing and UAV's motion degrees of freedom. Secondly, the attitude control law is designed based on the finite-time sliding mode observer and cascaded continuous sliding mode controller to eliminate the adverse effects of fuel sloshing and mass changing, and only using the measurable angles. Furthermore, aiming at the problem of power redundancy of the altitude channel, a memoryless non-linear altitude authority assignment controller based on vertical acceleration is proposed for improving the control performance. Finally, the simulation results of the waypoint flight illustrate the feasibility and effectiveness of the proposed control strategy.

A nonlinear wave coupling algorithm and its programing and application in plasma turbulences

The fully developed turbulence can be regarded as a nonlinear system, with wave coupling inside, which causes the nonlinear energy to transfer, and drives the turbulence to develop further or be suppressed. Spectral analysis is one of the most effective methods to study turbulence system. In order to apply it to the study of the nonlinear wave coupling process of edge plasma turbulence, an efficient algorithm based on spectral analysis technology is proposed to solve the nonlinear wave coupling equation. The algorithm is based on a mandatory temporal static condition with the nonideal spectra separated from the ideal spectra. The realization idea and programing flow are given. According to the characteristics of plasma turbulence, the simulation data are constructed and used to verify the algorithm and its implementation program. The simulation results and experimental results show the accuracy of the algorithm and the corresponding program, which can play a great role in the studying the energy transfer in edge plasma turbulences. As an application, the energy cascade analysis of typical edge plasma turbulence is carried out by using the results of a case calculation. Consequently, a physical picture of the energy transfer in a kind of fully developed turbulence is constructed, which confirms that the energy transfer in this turbulent system develops from lower-frequency region to higher-frequency region and from linear growing wave to damping wave.

Nonlinear Coupling of Reversed Shear Alfvén Eigenmode and Toroidal Alfvén Eigenmode during Current RampSupported by the National Key R&D Program of China (Grant No. 2017YFE0301900), the National Natural Science Foundation of China (Grant No. 11875233), and the China Postdoctoral Science Foundation (Grant No. 2020M670756).

Two novel nonlinear mode coupling processes for reversed shear Alfvén eigenmode (RSAE) nonlinear saturation are proposed and investigated. In the first process, the RSAE nonlinearly couples to a co-propagating toroidal Alfvén eigenmode (TAE) with the same toroidal and poloidal mode numbers, and generates a geodesic acoustic mode. In the second process, the RSAE couples to a counter-propagating TAE and generates an ion acoustic wave quasi-mode. The condition for the two processes to occur is favored during current ramp. Both the processes contribute to effectively saturate the Alfvénic instabilities, as well as nonlinearly transfer of energy from energetic fusion alpha particles to fuel ions in burning plasmas.

3D time-domain beam mapping for studying nonlinear dynamics in multimode optical fibers.

Characterization of the complex spatiotemporal dynamics of optical beam propagation in nonlinear multimode fibers requires the development of advanced measurement methods, capable of capturing the real-time evolution of beam images. We present a new space-time mapping technique, permitting the direct detection, with picosecond temporal resolution, of the intensity from repetitive laser pulses over a grid of spatial samples from a magnified image of the output beam. By using this time-resolved mapping, we provide, to the best of our knowledge, the first unambiguous experimental observation of instantaneous intrapulse nonlinear coupling processes among the modes of a graded index fiber.

Data-Based Optimal Tracking Control for Natural Gas Desulfurization System

Desulfurization control of natural gas has long been a challenging industrial issue owing to its inherent difficulty in establishing accurate mathematical model for the nonlinear and strong coupling process. In this paper, a data-based adaptive dynamic programming (ADP) algorithm is presented to solve optimal control for natural gas desulfurization. First, neural network (NN) is used to reconstruct the dynamics of the desulfurization system via the input and output production data. Then, an improved unscented Kalman filter (IUKF) aided ADP method is presented to solve optimal control problem for desulfurization system, where IUKF algorithm is developed as a new weight-updating strategy for the action network and the critic network. The IUKF aided algorithm can improve the convergence speed as well as the anti-interference ability of the ADP controller. Furthermore, the proposed IUKF-ADP algorithm is implemented using the heuristic dynamic programming (HDP) structure. Finally, the effectiveness of the proposed IUKF-ADP algorithm is demonstrated through experiments of the natural gas desulfurization system.

Generation of Multiband Chorus in the Earth's Magnetosphere: 1‐D PIC Simulation

AbstractMultiband chorus waves, where the frequency of upper band chorus is about twice that of lower band chorus, have recently been reported based on THEMIS observations. The generation of multiband chorus waves is attributed to the mechanism of lower band cascade, where upper band chorus is excited via the nonlinear coupling process between lower band chorus and the associated density mode with the frequency equal to that of lower band chorus. In this letter, with a one‐dimensional (1‐D) particle‐in‐cell (PIC) simulation model, we have successfully reproduced multiband chorus waves. During the simulation, the significant density fluctuation is driven by the fluctuating electric field along the wave vector of the pump wave (lower band chorus), which can be directly observed in this self‐consistent plasma system. Then, the second harmonic of the pump whistler‐mode wave (upper band chorus) is generated. After quantitatively analyzing resonant conditions among wave numbers, we can confirm that the generation is caused due to the coupling between the pump wave and the density fluctuation along its wave vector. The third harmonic can also be excited through lower band cascade if the pump whistler‐mode wave has a sufficiently large amplitude. Our simulation results not only provide a theoretical support to the mechanism of lower band cascade to generate multiband chorus but also propose a new pattern of evolution for whistler‐mode waves in the Earth's magnetosphere.

Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the ${d}^{0} ({\mathrm{CaTiO}}_{3})$ and ${d}^{1} ({\mathrm{LaTiO}}_{3})$ titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the ${A}_{g}$ or ${B}_{1g}$ mode amplitudes coupled to the ${A}_{u}$ or the ${B}_{3u}$ mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth ($\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\text{meV}$) and band gap ($\ensuremath{\sim}50$ meV). By comparing the coupling coefficients of undoped ${\mathrm{CaTiO}}_{3}$ and ${\mathrm{LaTiO}}_{3}$ to those for electron-doped $({\mathrm{CaTiO}}_{3})$ and hole-doped $({\mathrm{LaTiO}}_{3})$ titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the $d$ manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

Bicoherence analysis of streamer dynamics induced by trapped ion modes

High order spectral analyses have recently attracted a great deal of attention in the context of experimental studies for magnetic fusion. Among these techniques, bicoherence analysis plays an important role as it allows distinguishing between spontaneously excited waves and waves that arise from a coupling between different modes linked to specific physical mechanisms. Here, we describe and apply bicoherence analysis to kinetic simulations performed with reduced “bounce-averaged gyrokinetic” code, in order to investigate the nonlinear dynamics of trapped ion modes. This analysis shows a nonlinear wave coupling process linked to the formation of convective cells, thus furthers our understanding of the nonlinear energy transfer between turbulence structures in tokamaks.

Parametric excitation of ion-ion hybrid mode by a lower hybrid wave in a D-T plasma

Parametric excitation of ion-ion hybrid mode by a large amplitude lower hybrid wave in a two ion species D-T plasma is investigated. The sideband lower hybrid wave, generated in the nonlinear coupling process, beats with the pump to exert a parallel ponderomotive force on electrons driving the low frequency mode. The density perturbation associated with the latter couples with the $$\vec E \times \vec B$$ drift due to the pump to produce a nonlinear current driving the sideband. The ion-ion hybrid mode frequency in a 50:50 D-T plasma is close to geometric mean of deuterium and tritium cyclotron frequencies. The growth rate increases with the wave number of the mode. It also increases with the increase in the ratio of deuterium to tritium density.

Numerical Research on Dynamic Response of Underwater Vehicles in the Vertical Tube-Exit Stage

In the launching stage, the vehicle runs from the tube into the water above. This is a nonlinear and time-varying coupling process of water, structure and gas. This article aims at the dynamic response of the underwater vehicle in the vertical tube-exit stage. According to experimental pressure values on measuring points, the hydrodynamic pressure distribution on the vehicles surface is determined by Cosine Hypothesis. By LS-DYNA, the vehicles FEM model is built, and the hydrodynamic pressure is applied on the model. With numerical simulation, its dynamic response is obtained.

Stability analysis of polarization attraction in optical fibers

The nonlinear cross-polarization interaction among two intense counterpropagating beams in a span of lossless randomly birefringent telecom optical fiber may lead to the attraction an initially polarization scrambled signal towards wave with a well-defined state of polarization at the fiber output. By exploiting exact analytical solutions of the nonlinear polarization coupling process we carry out a linear stability study which reveals that temporally stable stationary solutions are only obtained whenever the output signal polarization is nearly orthogonal to the input pump polarization. Moreover, we predict that polarization attraction is acting in full strength whenever equally intense signal and pump waves are used.