Nonlinear Time-varying Research Articles

A framework for tracking changes in the intensity of investment funds' systemic risk

This study applies to investment funds a novel framework which combines marginal probabilities of distress estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology and the generalized dynamic factor model (GDFM). The framework models investment funds' distress dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures investment funds' systemic credit risk in three forms: (1) credit risk common to all funds within each of the seven categories the Eurosystem reports to the ECB; (2) credit risk in each category of investment fund conditional on distress on another category of investment fund and; (3) the buildup of investment funds' vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the investment funds' distress measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. The ranking of drivers of those common components in terms of importance differs from the ranking of the drivers of the common components of marginal measures of distress. This framework contributes to the formulation of macroprudential policy. • First study about the systemic credit risk in all types of investment funds (IF) • Contains a number of methodological features not applied to research on IF so far • Allows the estimation of measures of systemic credit risk for IF • Provides a structural early-warning measure of systemic vulnerabilities' build-up • Contributes to making macroprudential policy operational

Stabilizing a SISO LTI Plant With Gain and Delay Margins as Large as Desired

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of bounded-input bounded-output stabilizing any single-input single-output linear time-invariant controllable/observable plant with gain and time delay margins as large as desired; to do so, we propose the use of a non-linear time varying (NLTV) controller. Despite being NLTV, the proposed controller is relatively simple and the time variation is periodic; furthermore, the controller is noise tolerant, guarantees the exponential decay of the plant initial conditions, tolerates occasional jumps in the gain and delay and is robust to un-modelled dynamics.

Identification of ankle joint stiffness during passive movements--a subspace linear parameter varying approach.

This paper describes a novel method for the identification of time-varying ankle joint dynamic stiffness during large passive movements. The method estimates a linear parameter varying parallel-cascade (LPV-PC) model of joint stiffness consisting of two pathways: (a) an LPV impulse response function (IRF) for intrinsic mechanics and (b) an LPV Hammerstein cascade with time-varying static nonlinearity and a time-invariant linear dynamics for the reflex pathway. A subspace identification technique is used to estimate a statespace representation of the reflex stiffness dynamics. Then, an orthogonal projection decouples intrinsic from reflex response and subsequently identifies an LPV-IRF model of intrinsic stiffness. Finally, an LPV model of the reflex static nonlinearity is estimated using an iterative, separable least squares method. The LPV method was validated using experimental data from two healthy subjects where the ankle was moved passively by an actuator through its range of motion first without and then with perturbations. The identification results demonstrated that (a) the dynamic response of the intrinsic pathway changes systematically with joint position; and (b) the static nonlinearity of the reflex pathway resembles a half-wave rectifier whose threshold decreases and gain increases as ankle is moved to dorsiflexed position.

Delay-range-dependent stability criteria for delayed discrete-time Lur’e system with sector-bounded nonlinearities

This paper is devoted to the absolute and robust stability for uncertain discrete-time Lur’e systems with interval time-varying delays and sector-bounded nonlinearities. Both the cases with time-invariant and time-varying nonlinearities are considered. By dividing the variation interval of the time delays into some subintervals, some new delay-range-dependent robust stability criteria are derived in the form of linear matrix inequalities (LMIs) via a modified Lyapunov-Krasovskii functional (LKF) approach. The criteria are less conservative than some existing results. Finally, some numerical examples are presented to show the effectiveness of the proposed approach.

Un-symmetric input temperature control by using fuzzy sliding mode controller with gain auto-tuning

In order to obtain the desired product quality, temperature is an important control parameter in chemical and semiconductor manufacturing processes. Generally, the temperature control system has nonlinear time-varying, slow response speed, time-delay and un-symmetric control input dynamic characteristics. It is difficult to accurately establish the dynamic model for designing a general purpose temperature controller to achieve good control performance. Here a model-free fuzzy sliding mode control strategy is employed to design an intelligent temperature controller with gain-scheduling scheme or gain auto-tuning algorithm for a closed chamber with heater one-way input only. The concept of gain scheduling is employed to adjust the mapping ranges of the input and output fuzzy membership functions during the control process for improving the transient and steady-state control performances. The experimental results show that the steady state error of the step input response is always less than 0.2°C without overshoot by using this intelligent control schemes. It is suitable for industrial temperature control systems.

TORSION VIBRATION AND PARAMETRIC INSTABILITY ANALYSIS OF A SPUR GEAR SYSTEM WITH TIME-VARYING AND SQUARE NONLINEARITIES

This paper investigates the dynamics of a spur gear system with time-varying and square nonlinearities, by both analytical method and numerical simulation. First, the equations of motion of a 2 degree-of-freedom system are established and the harmonic balance method is used to analyze the stability and the steady-state response of the system under the main resonant condition. Then the perturbation method is used to analyze the parameter instability under the main, subharmonic and nonresonance conditions. Finally, the interactions between the main and subharmonic resonant amplitudes and the nonlinearity and the contact ratio are analyzed. The results reveal that the system response contains various frequency components, such as meshing frequency and its higher harmonic terms due to the nonlinearity and the time-varying stiffness. The existence of the time-varying meshing stiffness can also result in the subharmonic resonance, and even chaos through period-doubling bifurcations as the input torque increases.

Banking systemic vulnerabilities: A tail-risk dynamic CIMDO approach

This study proposes a novel framework which combines marginal probabilities of default estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology and the generalized dynamic factor model (GDFM) supplemented by a dynamic t-copula. The framework models banks’ default dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures banking systemic credit risk in the three forms categorized by the European Central Bank: (1) credit risk common to all banks; (2) credit risk in the banking system conditional on distress on a specific bank or combinations of banks; and (3) the buildup of banking system vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the banking sector short-term and conditional forward default measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. Finally, the framework produces robust out-of-sample forecasts of the banking systemic credit risk measures. This paper advances the agenda of making macroprudential policy operational.

Robust Evolving Fuzzy Adaptive Control With Input-domain Clustering

The paper proposes a fuzzy model reference adaptive control approach with evolving antecedent part. The proposed algorithm has the possibility of controlling a plant with poorly known and/or time-varying nonlinearity which is an advantage over approaches with fixed antecedent part. It is intended for control of a large class of nonlinear plant models with the dominant dynamics of the first order. Such plants occur quite often in process industries.

Stability and Observer Design for Lur'e Systems with Multivalued, Nonmonotone, Time-Varying Nonlinearities and State Jumps

This paper deals with the stability and observer design for Lur'e systems with multivalued nonlinearities, which are not necessarily monotone or time-invariant. Such differential inclusions model the motion of state trajectories which are constrained to evolve inside time-varying nonconvex sets. Using Lyapunov-based analysis, sufficient conditions are proposed for local stability in such systems, while specifying the basin of attraction. If the sets governing the motion of state trajectories are moving with bounded variation, then the resulting state trajectories are also of bounded variation, and unlike the convex case, the stability conditions depend on the size of jumps allowed in the sets. Based on the stability analysis, a Luenberger-like observer is proposed which is shown to converge asymptotically to the actual state, provided the initial value of the state estimation error is small enough. In addition, a practically convergent state estimator, based on the high-gain approach, is designed to reduc...

Fuzzy Adaptive Inverse Control for Pneumatic Loading System

The pneumatic loading system has the characteristics of time delay, time-varying and serious nonlinearity. In order to improve the control precision and overcome the shortcomings of traditional PI control algorithm, fuzzy adaptive inverse control is proposed to control the pressure of pneumatic loading system. Inverse model the pneumatic loading system off-line with fuzzy identification theory and get the initial inverse model. Take the initial inverse model as the initial controller to control the output pressure of the pneumatic loading system, and update the parameters of the controller online with the LMS filtering algorithm. Based on VC++ 6.0 software development platform, real-time control program is designed and tested on a pneumatic loading system. By comparing to the PI control algorithm, and fuzzy proportion, integration, differentiation control algorithm, the results prove that the proposed controller has high control accuracy, fast response and strong anti-disturbance ability for the pneumatic loading system.

Self-Adaptive PID Control of Hydraulic Quadruped Robot

Servo hydraulic system is important one of driving patterns of quadruped robot. While servo hydraulic system has characteristics of parameters time-varying and strong nonlinearity, so traditional PID control pattern cannot meet all the control demands well. To solve these problems, a set of control hardware is designed for a quadruped robot and a new control algorithm which can adjust PID parameters in real-time condition based on fuzzy control theory is proposed. By deducing transfer function, establishing system model and using MATLAB simulation tools to simulate the two algorithms, we compared the two algorithms and the simulation result turns out that compared with traditional PID control algorithm, the fuzzy PID control algorithm has features such as low overshoot, high stability precision, strong robustness. At the same time, the result turns out that the fuzzy PID control algorithm is much fitter for the joint control of quadruped robot.

Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity

An adaptive backstepping controller is constructed for a class of nonaffine nonlinear time-varying delay systems in strict feedback form with unknown dead zone and unknown control directions. To simplify controller design, nonaffine system is first transformed into an affine system by using mean value theorem and the unknown nonsymmetric dead-zone nonlinearity is treated as a combination of a linear term and a bounded disturbance-like term. Owing to the universal approximation property, fuzzy logic systems (FLSs) are employed to approximate the uncertain nonlinear part in controller design process. By introducing Nussbaum-type function, the a priori knowledge of the control gains signs is not required. By constructing appropriate Lyapunov-Krasovskii functionals, the effect of time-varying delay is compensated. Theoretically, it is proved that this scheme can guarantee that all signals in closed-loop system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighbourhood of the origin. Finally, the simulation results validate the effectiveness of the proposed scheme.

Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos.

Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

Improved robust stability criteria for a class of Lur'e systems with interval time-varying delays and sector-bounded nonlinearity

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

Filtering for Discrete-Time Stochastic Systems with Nonlinear Sensor and Time-Varying Delay

The filtering problem for a class of discrete-time stochastic systems with nonlinear sensor and time-varying delay is investigated. By using the Lyapunov stability theory, sufficient conditions are proposed to guarantee the asymptotical stablity with an prescribe performance level of the filtering error systems. These conditions are dependent on the lower and upper bounds of the discrete time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Research on Dynamic Models and Performances of Shield Tunnel Boring Machine Cutterhead Driving System

A general nonlinear time-varying (NLTV) dynamic model and linear time-varying (LTV) dynamic model are presented for shield tunnel boring machine (TBM) cutterhead driving system, respectively. Different gear backlashes and mesh damped and transmission errors are considered in the NLTV dynamic model. The corresponding multiple-input and multiple-output (MIMO) state space models are also presented. Through analyzing the linear dynamic model, the optimal reducer ratio (ORR) and optimal transmission ratio (OTR) are obtained for the shield TBM cutterhead driving system, respectively. The NLTV and LTV dynamic models are numerically simulated, and the effects of physical parameters under various conditions of NLTV dynamic model are analyzed. Physical parameters such as the load torque, gear backlash and transmission error, gear mesh stiffness and damped, pinions inertia and damped, large gear inertia and damped, and motor rotor inertia and damped are investigated in detail to analyze their effects on dynamic response and performances of the shield TBM cutterhead driving system. Some preliminary approaches are proposed to improve dynamic performances of the cutterhead driving system, and dynamic models will provide a foundation for shield TBM cutterhead driving system's cutterhead fault diagnosis, motion control, and torque synchronous control.

Application of Finite Element Model Updating and Reduction Techniques to Simulate Gearbox Bearing Faults

Simulation provides an effective method to generate vibration signals in the presence of machine faults such as in gears and bearings. Lumped parameter models (LPMs) and the LPM combined with a reduced finite element (FE) model of the casing were previously used to simulate localised and extended bearing faults in the inner and outer race. The analysis of the vibration signals based on the above techniques clearly indicated the presence of localised inner and outer race faults through envelope analysis in a high frequency band. However, the simulated results showed poor spectral matching over a wide frequency range when compared with the test results. There were also discrepancies in the low frequency region where extended faults in the outer and/or inner race interact with and modulate gear mesh frequencies. This paper describes FE-test correlation wherein the FE model of the gearbox casing is updated based on experimental modal analysis prior to the model reduction. The updated casing model is subsequently reduced using the Craig-Bampton method of component mode synthesis subject to the frequency range of interest. The greatly reduced mass and stiffness matrices are imported into a simulation model developed earlier which has the capability of simulating time-varying stiffness non-linearities and geometric faults for both gears and bearings.

Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.