Nonlinear Characteristics Of System Research Articles

Systematic simplification of the Anaerobic Digestion Model No. 1 (ADM1) – Model development and stoichiometric analysis

Rigorous process models provide a reliable basis for model-based monitoring and control of anaerobic digestion plants. Due to the complex model structure and non-linear system characteristics, the established Anaerobic Digestion Model No. 1 (ADM1) is rarely applied in industrial plant operation. The present investigation proposes a systematic procedure for successive model simplification and presents the description of five model variants of a mass-based ADM1. Individual model structures greatly differ in their number of implemented process phases, characteristic components and required parameters. Simplified model variants combine nutrient degradation and biogas formation based on first-order sum reactions, whereas complex model structures describe individual degradation pathways and intermediates during acido- and acetogenesis. Characteristic features of the derived model structures as well as the stoichiometric methane potentials and microbial biomass yields of the underlying degradation pathways of individual model variations are evaluated and discussed in detail.

Multiscale multidimensional recurrence quantitative analysis for analysing MEG signals in patients with schizophrenia

Schizophrenia is a very serious chronic disease with very high hazards. Its pathogenesis is still unclear, and searching for its potential biomarkers has always been a popular issue in the field of schizophrenia research. Nonlinear dynamic analysis of magnetoencephalogram (MEG) signals in patients with schizophrenia is helpful to solve this problem. To quantitatively analyse multiscale recurrence information of MEG signals in patients with schizophrenia, this investigation propose a novel approach termed the multiscale multidimensional recurrence quantitative analysis (MsMdRQA). We first employed two sets of model series, which were generated by Lorenz and Rössler systems, to test the effectiveness of MsMdRQA in nonlinear analysis and to analyse the effects of dimension. Then we applied MsMdRQA to analyse MEG signals in schizophrenia. The test results suggest that both the Lorenz system and the Rössler system have different recurrence states at different scales; therefore, they effectively reflect the internal structure information of the Lorenz system and the Rössler system. Furthermore, we found that the recurrence values of the MEG signals in patients with schizophrenia were significantly lower (p < 0.001) than those of healthy control subjects. Overall, MsMdRQA provides a better analysis method for exploring the nonlinear characteristics of complex systems with different scales.

Investigation on the parameter sensitivity of bladed assemblies undergoing mistuning features

The present study's objectives are primarily to reveal the mistuning effects on the coupling system's nonlinear vibration performance with a mechanical model of the flexible bladed disk system. And the sensitivities of the coupling system to different mistuning cases are also compared and estimated. Firstly, the tuned system's nonlinear characteristics are presented for providing a reference to interpret the nonlinear dynamics of the mistuning case. Then present analysis exploits the nonlinear response spectrum of the coupling system undergoing a series of parameter mistuning conditions. The numerical simulation reveals that the response characteristics of cycle blades exhibit perfect identity in the tuned system. When the parameter mistuning condition occurs, the identity characteristics are destroyed, especially the blade length mistuning case. The mistuning feature can also lead to new resonances at the modal frequency of flexible disk, which exhibits distinctive sensitivity to the different mistuning case. Besides, the vibration localization phenomenon occurs due to the broken cyclic periodicity of the bladed disk structure. Furthermore, enough attention should be paid to the coupling effects in the bladed disk system undergoing parameter mistuning in engineering practice.

Nonlinear dynamic analysis of ball screw feed system considering assembly error under harmonic excitation

In this study, a multi-degree-of-freedom dynamic model is developed to investigate the nonlinear dynamic characteristic of the ball screw feed system. The fourth-order Runge–Kutta method is used to obtain the numerical solution of the governing equations. In the proposed dynamic model, the assembly error of the system is considered as the deflection angle around the geometric center of the screw shaft. The motion of the system at each point is illustrated by displacement waveform, spectrum, phase diagram and Poincaré section. The influence of excitation amplitude and assembly error is discussed with excitation amplitude, deflection angle, and excitation frequency as control parameter in the bifurcation diagram and 3-D frequency spectrum. The results show that the assembly error has impacts on dynamic response, and the region of chaotic motion near resonance frequency broadens. Beyond that, an experiment is setup, and acceleration signals with different excitation frequencies and different excitation amplitudes are collected to validate the proposed model.

Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.

Identification and Control of Elongation System of Skin Passing Mill Based on Intelligent Algorithm

In view of the nonlinear, time-varying and time-delay characteristics of elongation control system of skin pass mill, according to analysis of the mechanism model of elongation control system of skin pass mill, BP neural network was used to identify the structural parameters of the model. With reference to the regulating function of biological immune system and the function of fuzzy reasoning logic which can approach nonlinear function, a fuzzy immune PID control strategy was proposed to improve the elongation control accuracy of skin pass mill combining fuzzy control and immune feedback mechanism with traditional PID control. The simulation results show that the control strategy has the advantages of small overshoot, fast response, strong anti-interference ability and robustness, and the control effect is better than the traditional control method.

Nonlinear dynamic analysis of supercritical and subcritical Hopf bifurcations in gas foil bearing-rotor systems

The Hopf bifurcation behavior is an important issue for the nonlinear dynamic analysis of gas foil bearing (GFB)-rotor systems. However, there is a lack of detailed study on different types of Hopf bifurcation and their corresponding characteristics for GFB-rotor systems. This paper is intended to provide a clear and systematic insight into the nonlinear dynamic characteristics of GFB-rotor systems with a supercritical or a subcritical Hopf bifurcation. The onset speed (OS) of instability (i.e., the bifurcation point) for the system is calculated by the linear stability analysis. The periodic solution of the system before or after the bifurcation point is obtained by the shooting method, and its stability is assessed by the Floquet multipliers. The shock stability and the unbalanced response characteristics of the GFB-rotor system with a supercritical or a subcritical Hopf bifurcation are presented. A GFB-rotor system with a supercritical Hopf bifurcation shows better dynamic characteristics than a system with a subcritical Hopf bifurcation. The parameter analysis reveals that the aspect ratio and the foil stiffness of the GFBs have obvious effects on the Hopf bifurcation type, while the loss factor has a relatively small effect. It is remarkable that although a lower foil stiffness increases the OS of instability, the actual speed limit would probably decrease as the Hopf bifurcation changes from a supercritical to a subcritical type. This can contribute to an understanding of the necessity of studies on actual available operating speed based on nonlinear analysis rather than conventional linear analysis for the bearing design.

Analysis of complex modal instability of a minimal friction self-excited vibration system from multiscale fractal surface topography

In order to reveal the stability and nonlinear characteristics of the friction self-excited vibration system from the perspective of microscopic multiscale fractal surface topography, a minimal two-degree-of-freedom mathematical model of the disc brake system is established in this paper. Considering the fractal characteristics of rough surface topography, the fractal contact stiffness of contact surfaces is introduced into the system model from the perspective of microscopic contact, and the effects of two important surface fractal parameters, fractal dimension D and fractal roughness G, on the stability and nonlinearity of the system are analyzed. Further finite element analysis and brake noise test improve the analysis of system stability and noise intensity by different surface topographies. The results show that the system stability can be improved with the increase of fractal dimension within a certain range, and the system will be in a stick state with the further increase of fractal dimension. With the increase of fractal roughness, the unstable modal coupling region of the system is increasing, which can reduce the stability of the system. The unstable region of the system is dependent on fractal dimension and fractal roughness, and has different sensitivity to them.

Nonlinear Vibration Mechanism of the Marine Rotating Machinery with Airbag Isolation Device under Heaving Motion

In this paper, we put an investigation into the nonlinear vibration mechanism of the marine rotating machinery with an airbag isolation device under heaving motion. First, we consider the effects of mass unbalance and heaving motion and propose a mathematical model of the marine rotating mechanical system with airbag vibration isolation. Then, the multiple-scale method is conducted to analyze the nonlinear dynamic characteristics of the mechanical system; the frequency-response curves are mainly studied under different parameters, such as the heave excitation, rotor speed, and damping; and the numerical method is also introduced to analyze its dynamic behaviors, such as the steady-state response and its corresponding phase diagram, Poincaré section. The dynamic stability of the system is investigated based on the bifurcations and the largest Lyapunov exponent about rotor speed and heaving frequency. The obtained results indicate complex nonlinear characteristics of the system compared to the system without heaving excitation, which can help us fully understand the dynamic characteristics and parametric optimization as well as structural design of the marine mechanical isolation system.

Modal analysis strategy and nonlinear dynamic characteristics of complicated aero-engine dual-rotor system with rub-impact

This paper aims to gain insight into the nonlinear modal characteristics and the possible influence of the modes on the responses for the practical dual-rotor system with rub-impact in aero-engine. The finite solid element method combined with a constraint stiffness model produced by rub-impact is introduced to build the governing equation of the complicated nonlinear dual-rotor system. In order to deal with the efficiency and numerical divergence in the process of solving the nonlinear modes of this large-scale nonlinear system, an analysis strategy is proposed by integrating a two-layer reduction technique into the harmonic balance method. The effectiveness of the analysis strategy is validated by applying to a simple rotor system, which can easily obtain the theoretical result. Based on the modeling method and analysis strategy, the modal characteristics of an aero-engine dual-rotor system with rub-impact are revealed. The results show that the modal frequency of the dual-rotor system increases when rub-impact occurs and has the feature of interval, which allows us to obtain the critical speeds of the rubbing system by traditional Campbell diagram. The rotation direction is an important factor since it can not only affect the gyroscopic effect but also change the friction effect of the rub-impact. It is found that the modal frequencies of the counter-rotation dual-rotor are less than those of co-rotation condition. More importantly, the forward modes of the counter-rotation dual-rotor may be instable when rub-impact occurs at a certain rotor, while the corresponding modes under the co-rotation condition are always stable. Furthermore, by analyzing the rubbing response of the dual-rotor, it is found that the modal characteristics have an important influence on rotor’s response. The instable forward modes existing in the counter-rotation dual-rotor may lead to the divergence of the response when passing the corresponding critical speed.

Power take-off damping control performance on the power conversion of oscillating-buoy wave energy converter

The power take-off (PTO) damping mechanism is very important to the motion and power conversion for the wave energy converters. Based upon the potential flow theory, the series expression with unknown Fourier coefficients of velocity potential function of the basin where the cylindrical floating buoy is located is obtained by using the eigenfunction expansion method. According to the characteristics of the PTO damper, the motion and wave energy conversion characteristics of the float under the linear and non-linear PTO damping are studied, respectively, and the over-damping problem under the linear PTO damping is emphatically explored. The results show that the influence of PTO system with low velocity index on the motion of the device is mainly reflected in the PTO damping coefficient. With the increase of damping coefficient, the resonance frequency of the wave energy device decreases gradually, but the decrease amplitude is very small. The non-linear characteristics of PTO system cannot change the optimal capture width ratio of the float, but the large velocity index can effectively improve the damping capacity of PTO system. At lower and higher frequencies, the optimal PTO damping obtained by the analytic algorithm will make the device in an over-damped state. The highest frequency in the low frequency part and the lowest frequency in the high frequency part which need to be modified will gradually decrease with the increase of radius and draught.

Research on Dynamic Balance of Spindle Rotor System Based on Particle Swarm Optimization

The dynamic balance is a significant issue for the nonlinear dynamic characteristics of the spindle rotor system. However, there is a problem that the dynamic balance is lacking detailed study on optimization method. In the paper, a modal dynamic balance optimization model of spindle rotor system is proposed, which can intend to improve the accuracy of spindle rotor system modal dynamic balance. Because the multiorder unbalance components are the main spindle rotor system mode shapes, the particle swarm optimization (PSO) method is adopted. The sum of squares of residual vibration after balancing is taken as the optimization objective, and the correction is presented as the optimization variable in the optimization model. The optimal correction weight of every unbalance component is calculated through a modal matrix equation of PSO. The vibration amplitude that is greatly reduced after optimization balance is presented under different conditions. The balancing effect shows a better dynamic characteristic than that of traditional methods. And the fluctuation range of the axis track of the rotor system also shows reductive phenomenon. The proposed optimization spindle rotor system model is well verified through experiments. It can contribute a theoretical optimization foundation for available dynamic balance in spindle rotor system.

Nonlinear Dynamic Characteristics of Automotive Gear Transmission System Based on Pure Torsion Model

With the rapid development of automobile industry, the performance requirements of gear transmission system are higher and higher. In order to improve the quality and reliability of gear transmission products, reduce the manufacturing cost of the whole vehicle and ensure the high-speed operation of the engine, it is necessary to carry out reasonable design, calculation and selection. In this paper, the gear transmission system is taken as the research object, the pure torsional vibration theory is studied, and the simulation analysis is carried out by MATLAB. The simulation results show that the automotive gear transmission based on the pure torsion model performs very well in the dynamic meshing force and the error is very small. This shows that the model can reduce the degree of gear wear.

State estimation for jump markov nonlinear systems of unknown measurement data covariance

For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable.

DSmT-based three-layer method using multi-classifier to detect faults in hydraulic systems

Fault identification in hydraulic valves is essential in maintaining the reliability and security of hydraulic systems. Due to the nonlinear characteristics of hydraulic systems under noisy working conditions, it is difficult to extract fault features from vibration signals collected from the surface of the valve body. Therefore, a DSmT-based three-layer method using multi-classifier is proposed to detect multiple faults occurred in hydraulic valves. Firstly, the raw signals are personalized to construct the training samples and the unknown testing samples. Secondly, a three-layer structure of the hybrid model called the layered hybrid model is constructed, which is suitable for hydraulic valves to detect the faults of different fault groups (including coil fatigue in the actuator and the abrasion inside the valve) and improve the diagnosis accuracy obviously. Finally, classification methods are selected to classify fault groups in the first two layers, and then the fault types are identified in the third layer by the fusion results using the Dezert-Smarandache Theory (DSmT). Experimental investigations are performed to validate the performance of the present method using a hydraulic valve (solenoid controlled pilot operated directional valve) controlled the hydraulic test rig. The results show that the average accuracy of detecting twelve types of faults is about 98.1%, which are better than those using other methods. It is expected that the present DSmT-based three-layer method using multi-classifier can be applied to more complex hydraulic systems.

Failure prediction by regularized fuzzy learning with intelligent parameters selection

Software failure time prediction, which is critical in software dependable evaluation, is among one of the most critical issues in software quality assurance research. Conventional software reliability predictions often use single models to illustrate the overall characteristic of the process of software failure. However, those models often fail to produce good prediction performance owing to the constant changes in software failure patterns during different time periods. Fuzzy systems like Takagi–Sugeno–Kang are multimodel approaches that combine simple submodels to represent the overall characteristic of dynamic nonlinear complex systems. This paper presents a novel Fuzzy system based software reliability prediction model, called regularized extreme learning adaptive neuro-fuzzy inference system, and employs the quantum-inspired binary gravitational search algorithm to determine its suitable regularization parameters. The new model can effectively reduce randomness, computational complexity as well as avoid local optimization when searching for optimal parameters. An experimentation using four real-world software failure data sets was carried out to compare the performance of the proposed model with that of certain representative software reliability prediction models. The results showed that the proposed model with the optimized parameters exhibits superior performance.

A self-organizing multi-model ensemble for identification of nonlinear time-varying dynamics of aerial vehicles

This article presents a novel identification approach which can deal with nonlinear and time-varying characteristics of complex dynamic systems, especially an aerial vehicle in the entire flight envelope. A set of local sub-models are first developed at different operating points of the system, and subsequently a self-organizing multi-model ensemble is introduced to aggregate the outputs of the local models as a single model. The number of employed local models in the proposed multi-model ensemble is optimized using a novel self-organizing approach. Also, wavelet neural networks, which combine both the universal approximation property of neural networks and the wavelet decomposition capability, are used as the local models of the proposed method. In addition, a generalized online sequential extreme learning machine is adopted in the introduced approach to determine the optimal validity function of the local models at each time step. Finally, the introduced self-organizing multi-model ensemble is applied to the NASA Generic Transport Model as a complex nonlinear system to demonstrate the effectiveness of the proposed identification approach. Furthermore, the results obtained from the conventional artificial neural networks are carefully compared with those from the wavelet neural networks, which are employed as the local models of the introduced multi-model ensemble. The simulation results suggest that the introduced wavelet neural network–based self-organizing multi-model ensemble can be used satisfactorily as the prediction model of model-based control systems for long prediction horizons.

Nonlinear dynamic characteristics of marine rotor-bearing system under coupled heave and pitch ship motions

The coupled heave and pitch motions of a ship sailing in head waves affect the stability of the marine rotor-bearing system. Based on the theory of analytical mechanics, this study establishes a dynamic model of the rotor-bearing system subjected to the coupled motions of heave and pitch, considering nonlinear oil film moments produced by the tilting of the rotor in the bearings. The nonlinear dynamic behaviours of the system are analysed using numerical methods to obtain Poincaré sections, bifurcation diagrams, and the largest Lyapunov exponents. The results show that dynamic bifurcation characteristics reveal complex quasi-periodic motion of upper and lower branches after the initial instability of the system, and the speed of second instability increase markedly. At high speeds, the amplitude of the rotor system increases sharply, which can cause the rotor to touch the inner wall of the bearings in the quasi-periodic state and a failure to transition to the chaotic state. Additionally, the effects of heave and pitch amplitude variations on the dynamic characteristics of the system are also discussed.

Application of Nonlinear Output Frequency Response Functions and Deep Learning to RV Reducer Fault Diagnosis

In this work, a new method based on the nonlinear output frequency response functions (NOFRFs) and deep convolution neural network (CNN) is proposed for RV reducer fault diagnosis. In order to solve the problem of low accuracy caused by output signal that cannot describe the nonlinear characteristics of system, the nonlinear spectrum based on output frequency response function is adopted. To improve the performance of error cost function model in back propagation (BP) process of CNN, a new comprehensive error cost function model is designed to guide the network parameters’ optimization in direction of the feature classification. Besides, an adaptive network structure optimization algorithm is proposed to avoid the blindness of network structure selection by experience. Specifically, 4-order NOFRF spectrums of system are first obtained by adaptive identification algorithm. Next, NOFRF spectrums are transformed into 2-D images, and CNN extracts the fault features hidden in spectrum images and performs fault classification. The experiment results indicate that the proposed method is effective for RV reducer fault diagnosis with the accuracy of 99.69%.

A swarm intelligence-based predictive regenerative braking control strategy for hybrid electric vehicle

Braking energy recovery is one of the main technologies affecting the economic performance of an electric vehicle. To improve economy from as much recovered braking energy as possible on the premise of ensuring vehicle security is the goal of regenerative braking control strategy. However, due to the non-linear and multi-objective characteristics of hybrid braking system, finding the optimal regenerative braking control strategy, considering safety, economy, and comfort, remains a challenge. Considering the efficient characteristics of regenerative braking system and battery aging, a swarm intelligence-based predictive regenerative braking control strategy is proposed. Particle swarm optimisation is used as the main part of the strategy, the ant colony algorithm is used to modify the iterative process of particle swarm optimisation to avoid convergence to a locally optimal solution, and model predictive control theory is applied in the control strategy to realise the optimal control. Then, under emergency braking conditions and urban cycling conditions, the stability and economy of proposed strategy are test by the simulation experiments. Finally, to reduce the computational complexity of the control strategy, an equivalent control strategy is proposed based on the nearest point method, and its effectiveness is verified by hardware-in-loop experiment.