Nonlinear Coupling Relationship Research Articles

Accurate Nonlinear Bending Analytical Solutions Setting New Benchmarks for Rectangular Thin Plates with Four Clamped Edges

The von Kármán plate equations have been challenging to solve accurately, especially for two-dimensional problems. This paper presents more accurate nonlinear analytical solutions for rectangular thin plates with four clamped edges, providing a new benchmark beyond Lévy’s solutions. The main features of the present method are that the deflection is expanded by the double series of the classical beam eigenfunctions, the Airy stress function satisfying the geometric deformation compatibility equation corresponds to the nonlinear coupling relationships between the plate deflection and the in-plane force and/or displacement boundary conditions. These solutions can verify existing nonlinear numerical and approximate analytical solutions, offering a robust basis for engineering design. The central deflection error is less than 0.01%, and the central stress error is below 0.6%, exceeding the accuracy of the existing literature.

Hybrid WARIMA-WANN algorithm for data prediction in bridge health monitoring system

Application of data-driven algorithm to model and predict the future trend of the structural health monitoring (SHM) data serves as important references for the future safety evaluation and decision-making of the bridges. An innovative hybrid WARIMA-WANN algorithm combining the Wavelet model, the autoregressive moving average (ARIMA) model and the artificial neural network (ANN) model is proposed to predict massive monitoring data in the bridge SHM system. The WPT serves as the decomposition function for the linear and nonlinear components of the hybrid model. The separated linear/nonlinear components are individually predicted with the ARIMA/ANN models and then combined to obtain the prediction values of the future data. The hybrid method is applied to predict the deflection values of a single-tower cable-stayed bridge. Multiple parameters in individual models are discussed and selected to increase the credibility of the prediction results for the example bridge. The results show that the proposed hybrid algorithm successfully captures the linear and nonlinear coupling relationships inside the SHM data from the frequency perspective of view and shows the best prediction performance when compared with the other four existing models. Different prediction steps obviously influence prediction performance due to the periodic nature of the bridge SHM data.

A quantitative causal analysis and optimization framework for inclusions of steel products

Inclusions generated during steelmaking and continuous casting processes could seriously reduce the mechanical properties of steel products and greatly increase the risk of corrosion failure. Much attention has been paid to perceiving the origin and classification of inclusions based on the process knowledge and mechanism model, while the value of industrial big data is underestimated. Machine learning (ML) methods have demonstrated potential in the processing of nonlinear and strong coupling relationships in industrial data. However, existing ML models are frequently unable to analyze causal relationships between manufacturing process, which is essential for the quality optimization. To address the limitation, this paper proposes a quantitative causal analysis and optimization framework. This framework starts with a feature selection module using propensity score matching (PSM) to measure the quantitative and reliable causal relationship between the process parameters and inclusions. Subsequently, a high-performance AutoML method, AutoGluon-Tabular (AGT), is applied to quantify the optimization range and verify the optimization effect. Specifically, AGT is used to estimate the inclusion level in each window of the process parameter to be optimized, choose the best window of which to determine adjustment strategies, and eventually verify the change of inclusion levels after optimization. The comparative experiments based on the real data collected from a steel company demonstrate that the proposed framework reduces the inclusion rate by 8.85%, which is effective, efficient and has guiding significance for the inclusions control of steel products.

Cosimulation of Bistable Permanent Magnet Circuit Breakers

The breaking and closing coils of bi-stable permanent magnet circuit breaker (PMCB) shares magnetic circuit, which leads to the fast time-varying nonlinear coupling relationship between the permanent magnetic field and the electromagnetic field, and between the breaking and closing magnetic circuits, which brings difficulty to its simulation. Aiming at the difficulty, this paper designs a new co-simulation method: First, the equivalent magnetic circuit of the bi-stable permanent magnet actuator (PMA) is established, and the ternary correspondence relationship of its electromechanical parameters is proved analytically for the first time. Then, the “equivalent electric circuit” of magnetic circuit in dynamic process of bi-stable PMA is proposed for the first time by analogy with the transformer model, and the calculation method of the time-varying parameters in this model is given. Finally, the “equivalent electric circuit” of magnetic circuit is used as a link, so the hardware circuit, software strategy and PMCB are connected together to form a point-by-point closed-loop co-simulation method. This simulation method can reflect the dynamic interaction between the electromagnetic field and the permanent magnetic field of the breaking and closing magnetic circuits, and also can reflect the dynamic interaction between the control module and the PMCB. So this method lays the foundation for simulation design of the high-performance bi-stable PMCB.

Formulation Optimization and Performance Prediction of Red Mud Particle Adsorbents Based on Neural Networks.

Red mud (RM), a bauxite residue, contains hazardous radioactive wastes and alkaline material and poses severe surface water and groundwater contamination risks, necessitating recycling. Pretreated RM can be used to make adsorbents for water treatment. However, its performance is affected by many factors, resulting in a nonlinear correlation and coupling relationship. This study aimed to identify the best formula for an RM adsorbent using a mathematical model that examines the relationship between 11 formulation types (e.g., pore-assisting agent, component modifier, and external binder) and 9 properties (e.g., specific surface area, wetting angle, and Zeta potential). This model was built using a back-propagation neural network (BP) based on single-factor experimental data and orthogonal experimental data. The model trained and predicted the established network structure to obtain the optimal adsorbent formula. The RM particle adsorbents had a pH of 10.16, specific surface area (BET) of 48.92 m2·g-1, pore volume of 2.10 cm3·g-1, compressive strength (ST) of 1.12 KPa, and 24 h immersion pulverization rate (ηm) of 3.72%. In the removal of total phosphorus in flotation tailings backwater, it exhibited a good adsorption capacity (Q) and total phosphorous removal rate (η) of 48.63 mg·g-1 and 95.13%, respectively.

Longitudinal vibration analysis and active disturbance rejection decoupling control of marine anticorrosive coatings Hybrid Propulsion Screw

The traditional manual methods of mixing paint, the construction process is difficult to ensure the quality and efficiency of the construction due to construction instability and error. To address this issue, we propose a novel approach to automatically mix and discharge marine anti-corrosion coatings using a Hybrid Propulsion Screw. The longitudinal vibration of the Hybrid Propulsion Screw (HPS) during operation is a critical factor that affects the mixing and discharge stability of anti-corrosion coatings. To analyze the vibration characteristics and stability of HPS during operation, we established a three-degree-of-freedom longitudinal vibration model of the HPS using the concentrated mass method and numerically solved it using the Runge-Kutta algorithm, and investigated the effects of external excitation and frequency on the longitudinal vibration of the system. Moreover, to reduce the fatigue damage caused by vibration, we introduced the Active Disturbance Rejection Decoupling Control (ADRDC) considering the nonlinear strong coupling relationship in HPS. And finally, we used the Fibonacci series to adjust the parameters of the Extended State Observer (ESO), and the simulation results demonstrate that our proposed approach is effective for controlling the longitudinal vibration amplitude of the system, which is of great significance for developing efficient and reliable screw stirring devices.

Information theory-based dynamic feature capture and global multi-objective optimization approach for organic Rankine cycle (ORC) considering road environment

Efficient capture and global optimization of organic Rankine cycle (ORC) operating features in road environment is the key to obtain actual waste heat recovery potential. The complexity of time-varying characteristics intensifies the nonlinear coupling relationship between ORC performance and parameters. This paper first designs and builds an ORC experimental system for recovering waste heat from internal combustion engine (ICE). The experimental system includes ICE and its measurement subsystem, ORC subsystem, expander lubrication subsystem, cooling subsystem, and ORC measurement subsystem. R245fa is used as working fluid; The expander adopts a specially designed single screw expander. The performance of ORC waste heat recovery is tested by adjusting the operating conditions of the ICE, expander, pump, and valve opening. The temperature range of waste heat is 627–686 K. Subsequently, a dynamic feature capture and global multi-objective optimization approach for ORC is proposed. The results show that the precision of dynamic feature capture can be improved at least 41.78% with the introduction of information theory in complex environment. Frequent fluctuation of vehicle speed is not conducive to the improvement of evaporator inlet temperature at working fluid side. As the speed of the vehicle is greatly reduced, the evaporator inlet temperature drops sharply. The frequent fluctuation of speed will intensify the nonlinear correlation between operating parameters and system performance and make the system performance more dependent on the coupling correlation between operating parameters. The approach proposed in this paper can provide a new idea for efficient capture of dynamic characteristics and global multi-objective optimization of ORC in road environment.

An Uncalibrated Image-Based Visual Servo Strategy for Robust Navigation in Autonomous Intravitreal Injection

Autonomous intravitreal injection in ophthalmology is a challenging surgical task as accurate depth measurement is difficult due to the individual differences in the patient’s eye and the intricate light reflection or refraction of the eyeball, often requiring the surgeon to first preposition the end-effector accurately. Image-based visual servo (IBVS) control does not rely on depth information, exhibiting potential for addressing the issues mentioned above. Here we describe an enhanced IBVS strategy to achieve high performance and robust autonomous injection navigation. The radial basis function (RBF) kernel with strong learning capability and fast convergence is used to globally map the uncertain nonlinear strong coupling relationship in complex uncalibrated IBVS control. The Siamese neural network (SNN) is then used to compare and analyze the characteristic differences between the current and target poses, thus making an approximation of the mapping relationships between the image feature changes and the end-effector motion. Finally, a robust sliding mode controller (SMC) based on min–max robust optimization is designed to implement effective surgical navigation. Data from the simulation and the physical model experiments indicate that the maximum localization and attitude errors of the proposed method are 0.4 mm and 0.18°, exhibiting desirable accuracy with the actual surgery and robustness to disturbances. These results demonstrate that the enhanced strategy can provide a promising approach that can achieve a high level of autonomous intravitreal injection without a surgeon.

Energy storage optimization of ferroelectric ceramics during phase-transition process of amorphous/nanocrystalline and polycrystalline by using a phase-field model for dielectric breakdown

Ferroelectric ceramics have the potential to be widely applied in the modern industry and military power systems due to their ultrafast charging/discharging speed and high energy density. Considering the structural design and electrical properties of ferroelectric capacitor, it is still a challenge to find out the optimal energy storage of ferroelectric ceramics during the phase-transition process of amorphous/nanocrystalline and polycrystalline. In this work, a finite element model suitable for the multiphase ceramic system is constructed based on the phase field breakdown theory. The nonlinear coupling relationship of multiple physical fields between multiphase ceramics was taken into account in this model. The basic structures of multiphase ceramics are generated by using the Voronoi diagram construction method. The specified structure of multiphase ceramics in the phase- transition process of amorphous/nanocrystalline and polycrystalline was further obtained through the grain boundary diffusion equation. The simulation results show that the multiphase ceramics have an optimal energy storage in the process of amorphous polycrystalline transformation, and the energy storage density reaches the maximum when the crystallinity is 13.96% and the volume fraction of grain is 2.08%. It provides a research plan and idea for revealing the correlation between microstructure and breakdown characteristics of multiphase ceramics. This simulation model realizes the nonlinear coupling of the multiphase ceramic mesoscopic structure and the phase field breakdown. It provides a reference scheme for the structural design and performance optimization of ferroelectric ceramics.

Operational characteristics and optimization of Hydro-PV power hybrid electricity system

Hydropower is the largest capacity and most realistic way to regulate photovoltaic (PV) power fluctuation at present. However, the stability issue of hydropower unit caused by the volatility of PV power comes to be concerned. A novel model of hydro-PV power hybrid system considering the high-order nonlinear coupling relationship of hydraulic, mechanical, electrical factors of hydropower unit, is proposed in this paper, which contains two multi-objective functions, two capacity indexes, two control strategies, and two computational models. The control strategies with power complementary control (PCC) and primary frequency control (PFC) promote hydropower smoothes the fluctuation of PV power, but the volatility of PV power increases the risk of instability of hydropower units. Furthermore, under the premise that hydropower undertakes dual tasks: regulating load demand and compensating PV power, the stability and power quality of the hybrid system are guaranteed when β is within 60%. If hydropower unit is only responsible for compensating PV power, β will increase slightly. Once PV power exceeds the regulation capacity of hydropower, it will lead to the oscillation of hydro-PV power hybrid electricity system (HPP-HES), threatening the safety of HPP-HES and power grid.

Collaborative Antiswing Hoisting Control for Dual Rotary Cranes With Motion Constraints

With large load capacity and flexible payload attitude adjustment capability, dual rotary cranes (DRCs) play crucial roles in infrastructure construction with heavy hoisting demands. However, as a kind of collaborative control systems, DRCs have complex collaborative constraints, and large-scale payloads cannot be simply regarded as mass points; moreover, due to the lack of control inputs, some state variables can only be indirectly controlled through complicated nonlinear coupling relationships, which make the controller design and corresponding analysis particularly difficult. Additionally, in practical applications of DRCs, many factors (such as boom motion overshoots, inaccurate gravity (torque) compensation, etc.) are prone to result in unexpected steady errors, large payload swing, and boom collisions, which may result in inaccurate assembly, and even lead to safety accidents. To this end, this article proposes an adaptive nonlinear proportional-integral-derivative-like collaborative control method for DRCs, which can realize accurate and efficient antiswing hoisting. To our knowledge, this is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> controller embedded with integral terms <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization during the controller design or stability analysis, which can effectively reduce steady errors, and keep boom motions within safety ranges by adaptive gravity (torque) compensation and elaborately designed constraint terms. Theoretically, the closed-loop stability and convergence are proven through strict mathematical analysis by using Lyapunov techniques and LaSalle’s invariance theorem. Finally, several groups of hardware experimental results are presented for effectiveness and robustness verification.

Inferring Flight Performance Under Different Maneuvers With Pilot’s Multi-Physiological Parameters

The relationship between flight performance and multi-physiological parameters under different flight operating patterns is unknown. This work proposes a Stacked Gaussian Process Network (SGPN) to reveal it. SGPN is a multi-layer network model formed by recursion from a regular Gaussian process and random disturbance. This work constructs an auxiliary variable strategy with the induced points to improve its learning efficiency, thus leading to a sparse SGPN model. In it, a Gaussian process acts as an activation function of each node, but the entire model is no longer a Gaussian process and thus very challenging to solve it. This work presents its solution via variational approximate inference. Experimental results of pilot flight performance evaluation show that the proposed model has stronger learning and generalization ability than its seven competitive peers. It is able to approximate non-linear coupling relationship between multi-physiological parameters and flight height differences.

Multiobjective Optimization for a Li-Ion Battery and Supercapacitor Hybrid Energy Storage Electric Vehicle

The acceptance of hybrid energy storage system (HESS) Electric vehicles (EVs) is increasing rapidly because they produce zero emissions and have a higher energy efficiency. Due to the nonlinear and strong coupling relationships between the sizing parameters of the HESS components and the control strategy parameters and EV’s performances, energy consumption rate, running range and HESS cost, how to design the HESS EVs for different preferences is a key problem. How to get the real time performances from the HESS EV is a difficulty. The multiobjective optimization for the HESS EV considering the real time performances and the HESS cost is a solution. A Li-ion battery (BT) semi-active HESS and optimal energy control strategy were proposed for an EV. The multiobjectives include energy consumption over 100 km, acceleration time from 0–100 km per hour, maximum speed, running range and HESS cost of the EV. According to the degrees of impact on the multiobjectives, the scaled factors of BT capacity, the series number of Li-ion BTs, the series number of super-capacitors (SCs), the parallel number of SCs, and charge power of the SCs were chosen as the optimization variables. Two sets of different weights were used to simulate the multiobjective optimization problem in the ADVISOR software linked with MATLAB software. The simulation results show that some of the multiobjectives are sensitive to their weights. HESS EVs meeting different preferences can be designed through the weights of different objectives. Compared with the direct optimization algorithm, the genetic algorithm (GA) has a stronger optimization ability, and the single objective is more sensitive to its corresponding weight. The proposed optimization method is practical for a Li-ion BT and SC HESS EV design.

Optimization of injection molding process parameters based on GA-ELM-GA

The most common optimization method for the optimization of injection mold process parameters is range analysis, but there is often a nonlinear coupling relationship between injection molding process parameters and quality indicators. Therefore, it is difficult to find the optimal process combination in range analysis. In this article, a genetic algorithm optimized extreme learning machine network model (GA-ELM) combined with genetic algorithm (GA) was proposed to optimize the process parameters of the injection mold. Take the injection molding process parameter optimization of an electrical appliance buckle cover shell as an example. In order to find the process parameters corresponding to the minimum warpage deformation, an orthogonal experiment was designed and the results of the orthogonal experiment were analyzed. Then, the corresponding optimal process combination and the degree of influence of process parameters on the warpage deformation were obtained. At the same time, the extreme learning machine network model (GA-ELM) optimized by the genetic algorithm was used to predict the warpage deformation of the plastic part. The trained GA-ELM model can map non-linear coupling relationship between the five process parameters and the warpage deformation well. And the optimal process parameters in the trained GA-ELM network model was searched by the powerful optimization ability of genetic algorithm. Generally speaking, the warpage deformation after optimization by range analysis is reduced by 6.7% compared with the minimum warpage after optimization by orthogonal experiment. But compared to the minimum warpage deformation after orthogonal experiment optimization, the warpage deformation after GAELM-GA optimization is reduced by 22%, which is better than that of the range analysis, thus verifying the feasibility and the optimization of the optimization method. This optimization method provides a certain theoretical reference and technical support for the field involving the optimization of process parameters.

A bi-cyclic co-optimization method for sizing of electricity-hydrogen hybrid energy storage microgrid

Due to the nonlinear and strong coupling relationships between the sizing parameters of the microgrid components and the operation strategy parameters, this paper proposes a bi-cycle co-optimization method for optimal sizing the microgrid components cost-effectively.

An Adaptive Nonsingular Fast Terminal Sliding Mode Control for Yaw Stability Control of Bus Based on STI Tire Model

Due to the bus characteristics of large quality, high center of gravity and narrow wheelbase, the research of its yaw stability control (YSC) system has become the focus in the field of vehicle system dynamics. However, the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research. In this paper, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads. Firstly, the STI (Systems Technologies Inc.) tire model, which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force, is established based on experimental data and firstly adopted in the bus YSC system design. On this basis, a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM, which has the merits of fast transient response, finite time convergence and high robustness against uncertainties and external disturbances, is designed. Thirdly, to solve the optimal allocation problem of the tire forces, whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire, the robust least-squares allocation method is adopted. To verify the feasibility, effectiveness and practicality of the proposed bus YSC approach, the TruckSim-Simulink co-simulation results are finally provided. The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved. This research proposes a more effective design method for bus YSC system based on a more accurate tire model.

Adhesion of elastic wavy surfaces: Interface strengthening/weakening and mode transition mechanisms

Surface roughness involved in elastic adhesion of solids may lead to an unstable loading process, which makes experimental characterization and theoretical modeling full of challenge. The full self-consistent model (FSCM) is the most accurate adhesion contact model in the continuum framework, but the strongly nonlinear coupling relationship between surface gap and interaction is very difficult to solve even with high-precision numerical calculation. In this paper, several techniques including the arc-length control method, the Riemann–Stieltjes integral, the adaptive mesh and the Newton–Raphson iterative method were employed in a new solving program to overcome the difficulty of numerical calculation. This calculation method has high efficiency and precision, and it gives a full force–displacement curve containing all possible stable and unstable equilibrium states. The full force–displacement curves for the adhesive contact of wavy surfaces are zigzag and some additional oscillations or minor roundabouts are observed, which have not been detected in the extended JKR and Maugis–Dugdale models. With the increase of surface roughness, the pull-off force first increases and then decreases, because the adhesion mode transforms from the simple contact mode to the multiple one. It is found that the pressure oscillation induced by waviness leads to interface strengthening for small roughness, and the limitation of the theoretical strength and the development of interface cavitation result in interface weakening for large roughness. Compared to the FSCM, the JKR theory significantly overestimates the pull-off forces for large surface roughness. The extended Maugis–Dugdale model is also invalid for large roughness, and if the step cohesive stress is determined by applying a condition of the identical pull-off force at the rigid limit, it can work well for small roughness.

Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism.

The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton–Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived. The VDEs and Newton–Euler equations constitute the IDEs of the system. Finally, the explicit recursive algorithm for solving the quaternion in the equation is given in the phase space. Then the IDEs are solved by substituting the quaternion into the dynamic equations in the configuration space. The predicted numerical results of the established FDEs and IDEs are verified by comparing with virtual and actual experimental data. The actual experiment shows that the relative errors of the FDEs and the IDEs constructed in this article are 2.21% and 7.65%, respectively. This research provides a new strategy for further improving the practicability of the six-axis accelerometer.

Coordinated optimization control of shield machine based on dynamic fuzzy neural network direct inverse control

During shield machine tunneling, the earth pressure in the sealed cabin must be kept balanced to ensure construction safety. As there is a strong nonlinear coupling relationship among the tunneling parameters, it is difficult to control the balance between the amount of soil entered and the amount discharged in the sealed cabin. So, the control effect of excavation face stability is poor. For this purpose, a coordinated optimization control method of shield machine based on dynamic fuzzy neural network (D-FNN) direct inverse control is proposed. The cutter head torque, advance speed, thrust, screw conveyor speed and earth pressure difference in the sealed cabin are selected as inputs, and the D-FNN control model of the control parameters is established, whose output are screw conveyor speed and advance speed at the next moment. The error reduction rate method is introduced to trim and identify the network structure to optimize the control model. On this basis, an optimal control system for earth pressure balance (EPB) of shield machine is established based on the direct inverse control method. The simulation results show that the method can optimize the control parameters coordinately according to the changes of the construction environment, effectively reduce the earth pressure fluctuations during shield tunneling, and can better control the stability of the excavation surface.

Two-dimensional analytical investigation into energy conversion and efficiency maximization of magnetohydrodynamic swirling flow actuators

The azimuthal Lorentz-force-driven magnetohydrodynamic swirling flow between coaxial cylindrical electrodes with an imposed axial magnetic field has extensive application in the swirling actuators. To identify the mechanism of energy conversion within the flow-discharge nonlinearly coupled field, we develop a 2-D analytical functional model bridging the gap between the imposed magnetic field distribution and the magnetohydrodynamic fields. With Hall effect present, the analytical solution is found to be controlled by the Reynolds number and a newly defined dimensionless number (K) deduced from the Hartmann number and the Hall parameter. The solution is confirmed with numerical and experimental results. By virtue of its analytic nature, the model provides more convenient insight and understanding into energy coupling and efficiency optimization. Based on this model, the nonlinear coupling relationship between the total voltage and the electromotive force is identified. The most striking contribution is the identification of double barriers, induced by Hall effect and viscosity, to maximize system efficiency through the model. To achieve efficiency maximization, the optimum magnetic field distribution is found by solution of the functional extremum problem derived from the analytical model.