Output frequency response function-based analysis for nonlinear Volterra systems

In this Chapter, An extension of the existing frequecncy analysis and design techniques is discussed to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems. The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced for the frequency analysis and design of nonlinear systems.

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

Theory of nonlinear systems

Analysis of fast-sampled non-linear systems: generalised frequency response functions for δ-operator models

Theory of nonlinear control

The identification of block-oriented systems represented by interconnections of linear dynamic systems and non-memory nonlinear elements have been of great importance for control and for analysis of biological nonlinear systems. In this study, two new algorithms to obtain structural models of nonlinear systems using numerically-given (experimentally obtained) Volterra kernels are proposed. One is to determine the parallel factorable base model; a sum of subsets, each of which has a parallel structure of linear dynamic systems whose outputs are multiplied. Another is called the Sm model; linear dynamic systems and nonlinear power elements in cascade. The results of numerical experiments showed that both methods could be practically useful for identifications and analysis of nonlinear systems.

The analysis of multidegree-of-freedom (MDOF) nonlinear systems is studied using the concept of nonlinear output frequency response functions (NOFRFs), which are a series of one-dimensional functions of frequency recently proposed by the authors to facilitate the analysis of nonlinear systems in the frequency domain. By inspecting the relationships between the NOFRFs of two consecutive masses in the locally nonlinear MDOF systems, a series of properties about the NOFRFs of the nonlinear systems are obtained. These properties clearly reveal how the system linear characteristic parameters govern the distribution of nonlinear effects induced by the system nonlinear component within the whole systems. The results obtained in the present work are of significance to the frequency response analysis for nonlinear systems. One important potential application of these results is the detection and location of damages in engineering structures, which make the structures behave nonlinearly.

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

On the application of diakoptics to nonlinear systems

Nonlinear [formula omitted]-gain verification for nonlinear systems

The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was introduced in [1] for the analysis of nonlinear systems in the frequency domain where a least-squares (LS) method was proposed for the evaluation of the NOFRFs using system input-output data. However, this leastsquares (LS) based approach may experience numerical errors due to matrix inversion and consequently cannot produce accurate NOFRFs sometimes. In order to mitigate this problem, in the present study, a modified LS method (M-LS) is proposed to make sure that the information matrix to be inverted for the LS solution is appropriately constructed so as to improve the condition number of the information matrix and reduce the numerical errors. Simulation results have demonstrated the effectiveness of the newly proposed method and indicated that the new method will enable a more accurate evaluation of the NOFRFs and facilitate the frequency analysis of nonlinear systems directly using system input-output data.

A symplectic numerical approach to the stability analysis of nonlinear parametric excited systems with multi-degree-of-freedom is developed and the stability of a nonlinear vibration system depends on the dynamic behavior of its perturbation. The nonlinear parameter-varying differential equations for the perturbation motion are expressed in the form of Hamiltonian equations with time-varying Hamiltonian, and are converted further into the classical Hamiltonian equations with extended time-invariant Hamiltonian by augmenting the state variables. The solution to the augmented Hamiltonian equations has the symplectic structure in terms of the symplectic transformation. Then the difference equations of the symplectic Runge-Kutta algorithm with a sufficient condition are constructed, which is proved to preserve the intrinsic symplectic structure of the original solution. In particular, the symplectic Gauss-Runge-Kutta algorithm with stage 2 and order 4 is proposed and applied to the stability analysis of a nonlinear system. Unstable regions based on the nonlinear periodic-parameter perturbation equation are obtained by using the symplectic Gauss-Runge-Kutta algorithm, analytical solution method and non-symplectic conventional Runge-Kutta algorithm to verify the higher accuracy of the proposed algorithm. Unstable regions based on the nonlinear perturbation are given to illustrate the improvement over those based on the linear perturbation. The developed symplectic approach to the stability analysis can preserve the symplectic structure of the original system and is applicable to nonlinear parametric excited systems with multi-degree-of-freedom.

A copula-based Gaussian mixture closure method for stochastic response of nonlinear dynamic systems

A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure