Hierarchical Classifier-Regression Ensemble for Multi-phase Non-linear Dynamic System Response Prediction: Application to Climate Analysis

Seasonal variability is the complex non-linear response of the physical climate system. There are two types of natural variability: those external and internal to the climate system. In any given season, natural variability may cause the climate to be different than its long-term average. This study examines with the seasonal variation of the maximum temperatures during the summer season. In addition, the maximum temperatures in May become close to the characteristics of the summer season. The monthly data for maximum temperature of May, June and July were used from Iraqi Meteorological Organization and Seismology (IMOS) for 47 years from 1970 to 2017 for Baghdad city. This period was long enough to estimate the range of approaching maximum temperature (Tmax) May to summer. Results revealed a significant Tmax for Baghdad during the second period (1992–2017) and ?shown similar behavior of Tmax in May to June and July; on the contrary that first period (1970–1991). In second period, two phases have been found out, positive phase and negative phase. The positive phase were happened in 1995, 1999, and 2006, and the negative phase was four cases (1992, 2004, 2013, and 2016), while a few cases recorded in first period. The amplitudes of monthly variability had same distance of leaner correlation especially in 1999 and 2013 that represent coherent wave with summer seasons. The variance difference for Tmax between May and June approximately was 2°C for second study’s period, while exceed this range in first period. This variance change to 7.5°C when found difference between July and May.

Geometrically nonlinear transverse steady-state periodic forced vibration of multi-degree-of-freedom discrete systems with a distributed nonlinearity

In this research the seismic response of structures isolated at the base by means of High Damping Laminated Rubber Bearings (HDRB) is evaluated. The analysis is performed by using a stochastic approach and a Gaussian zero mean non stationary stochastic process is used in order to model the seismic acceleration acting at the base of the structure. In order to take into account of the non-linear constitutive behavior both of the base isolation device and of the structure, the hysteretic differential Bouc-Wen model (BWM) is adopted. Moreover, the stochastic linearization method in the time domain is adopted to estimate the statistical moments of the non-linear system response in the state space. After estimating the system response variance a sensitivity analysis is carried out. The final aim of the research is to asses the real capacity of base isolation devices in order to protect the structures from seismic actions, by avoiding a non-linear response with associated large plastic displacements, and, therefore, by limiting related damage phenomena in structural and non structural members. In order to achieve this objective the stochastic response of a non-linear n-dof shear-type base isolated building is analyzed. The protection level offered to the structure by the base isolators is then assessed by evaluating the reduction both of the displacement response and the hysteretic dissipated energy.

Predicting nonlinear dynamic response of internal cantilever beam system on a steadily rotating ring

We theoretically investigated the nonlinear near-resonance electromagnetic response of quantum dot systems caused by interlevel electron transitions. The effect of electron-electron (e–e) interaction in the systems on the response was taken into account by the use of a self-consistent field approach in the quasi-static limit within the density matrix formalism under stationary conditions. Analysis and numerical simulations showed the possibility of realizing the intrinsic optical bistability in quantum dot systems due to the e–e interaction. The results obtained could find application in design, fabrication, and exploitation of all-optical quantum dot-based switches.

This study is aimed at investigating the effects of intermediate support stiffness on nonlinear vibration response of transmission system. A coupled bending–torsional–lateral dynamic model with 14 degrees of freedom of transmission system is proposed comprehensively considering rubber dynamic stiffness, time-varying stiffness, static transmission error, and backlash. Meanwhile, a model of intermediate support with rubber nonlinear properties is developed to improve the accuracy of analysis. On the basis of the nonlinear differential equations derived by the lumped-parameter method, the dynamic responses of the key parts in the transmission system are obtained using the Runge–Kutta method and the effects of intermediate support stiffness on the dynamic characteristics are analyzed. Numerical results show that complicated interaction occurs and intermediate support stiffness has a great influence on the vibration of the coupled system. With the increase in the intermediate support stiffness, the vibration displacements in the three directions of the gear are progressively reduced and the nature frequencies are changed. The influence of the radial stiffness is greater than that of the axial stiffness. An experiment is performed subsequently to validate the effect of intermediate support stiffness on system, and the experimental results are consistent with numerical ones.

In the previous paper, the authors described the statistical studies on the response of nonlinear control systems subjected to an ergodic stationary Gaussian random input. This paper is devoted to the fundamental approaches to the non-stationary random time series which are considered to arise quite often for the automatic control systems in practice. Firstly, the response of nonlinear control systems subjected to a non-stationary random signal is evaluated. Secondly, for an example, a non-stationary Orenstein-Uhlenbeck process which is obtained by using the method of Fokker-Planck is treated. Detail illustrations are shown by several examples.

In recent years, the non-stationary random processes have attracted considerable attentions in the field of adaptive or self-optimizing control, but little seems to have been done for those cases. In this paper, a very simple but fundamental case of non-stationary random process of response of nonlinear control systems is treated. That is, the analytical study on the evaluation of the response of nonlinear control systems subjected to a suddenly applied stationary random signal is described The two methods are established here by introducing some extensive method of the equivalent linearization technique. A graphical method for evaluating the non-stationary random response is proposed and such procedures are explained by typical examples in detail.

Least absolute deviation (LAD) is a well-known criterion to fit statistical models, but little is known about LAD estimation in structural equation modeling (SEM). To address this gap, the authors use the LAD criterion in SEM by minimizing the sum of the absolute deviations between the observed and the model-implied covariance matrices. Using Monte Carlo simulations, the authors compare the performance of this LAD estimator along several dimensions (bias, efficiency, convergence, frequencies of improper solutions, and absolute percentage deviation) to the full information maximum likelihood (ML) and unweighted least squares (ULS) estimators in structural equation modeling. The results for LAD are mixed: There are special conditions under which the LAD estimator outperforms ML and ULS, but the simulation evidence does not support a general claim that LAD is superior to ML and ULS in small samples.

The 2011 issue of Nonlinear Dynamics presents articles on stability of non-linear dynamic structures and systems. Alijani and co-researchers investigate geometrically nonlinear vibrations of rectangular plates with Functionally Graded Materials (FGM) in thermal environments via a multi-modal energy approach. Demeio and co-researchers investigate the primary non-linear resonance response of a one-dimensional continuous system, which can be regarded as a model for semiinfinite cables resting on an elastic substrate reacting in compression only, and subjected, to a constant distributed load and to a small harmonic displacement applied to the finite boundary. Stoykov and Ribeiro investigate the geometrically non-linear periodic vibrations of beams with rectangular cross section under harmonic forces using a p-version finite element method. Krylov and co-researchers investigate the feasibility of two-directional switching of an initially curved or prebuckled electrostatically actuated micro-beams using a single electrode fabricated from the same structural layer.

Complex behavior in nonlinear dynamical systems often arises from resonances, which enable intricate energy transfer mechanisms among modes that otherwise would not interact. Theoretical, numerical and experimental methods are available to study such behavior when the resonance arises among modes of the linearized system. Much less understood are, however, resonances arising from nonlinear modal interactions, which cannot be detected from a classical linear analysis. Academic examples of such phenomena have been known, but no systematic method has been developed to detect and model nonlinear resonant interactions purely from numerical or experimental data. Here, we develop such a data-driven methodology that identifies nonlinear resonant response on low-dimensional spectral submanifolds (SSMs) of the dynamical system. Our approach is generally applicable to nonlinear resonances, but we specifically focus here on one particular behavior: subharmonic response in forced nonlinear systems without any resonance among the linearized frequencies of the unforced system. We first illustrate analytically how such a response is born out of a nonlinear resonance hidden in the conservative limit of the system. We then show how this effect can be identified and modeled purely from data. As our main example, we isolate and model previously unexplained response patterns in fluid sloshing experiments.

Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

Among the irregular responses of nonlinear dynamic systems, chaotic responses of nonlinear systems are probably the most attractive phenomena along with the new observations in the last decades. A nonlinear deterministic system may behavior chaotically under regular such as periodic excitations. Regular motion of a system subjected to periodic exertions is usually periodic. In contrast with regular motions, final states of chaotic vibrations are extremely nonperiodic. This research is to analyzing the irregular behavior of dynamic systems with implementation of a newly developed criterion named Periodicity-Ratio. The development of a methodology for diagnosing the irregular motions from the regular motions of a dynamic system is presented. The Periodicity-Ratio describes the degree of periodicity of motion and can be conveniently used to distinguish a nonperiodic motion from a regular vibration or oscillation and to diagnose whether or not a motion is chaotic and the other irregular responses of the nonlinear dynamic systems, without plotting any figures. The analyses on the irregular behavior of nonlinear dynamic systems with the implementation of the Periodicity-Ratio will be demonstrated.

The consistency of a nonlinear system's response to a repeated complex waveform drive signal is an important consideration in classical and quantum systems as diverse as lasers, neuronal networks, and manufacturing plants. We show from a consideration of different characteristic waveforms that there is typically an optimal drive amplitude for the most consistent response; internal noise sources dominate for small amplitude driving while deterministic system nonlinearity reduces consistency for large amplitudes. We test this general concept and its measurement experimentally and numerically on the specific example of a laser system.

ABSTRACTThis paper addresses the identification of Nonlinear (NL) systems using a linearization approach, introducing a combined estimator to tackle this challenge. We assume that the unknown NL system operates around a stable, slowly varying (nominal) operating point. The system trajectory is then perturbed slightly via small input perturbations. While the system's operating point evolves slowly over time, the small (broadband) input signal excites the system dynamics. We demonstrate that the NL system's response to these small perturbations can be approximated by a Linear Parameter‐Varying (LPV) system model. Furthermore, we show that this LPV model represents the linearized version of the unknown NL system around the operating point. A new parametrization for the LPV model coefficients, referred to as “gradient‐parameterized” LPV coefficients, is introduced, establishing a structural relationship between the coefficients. This structural relationship reduces the number of parameters to be estimated and ensures that the LPV model always corresponds to the linearized form of the NL system. Additionally, we demonstrate that this LPV model structure allows for the unique reconstruction of the NL system model through symbolic integration, resulting in a closed‐form nonlinear Ordinary Differential Equation (ODE). This integration introduces a second structural relationship, linking the LPV model to the NL model. By leveraging these two structural relationships, we reformulate the problem of NL system identification via linearization as a combined estimation problem, leading to a unified LPV‐NL estimation framework. This approach utilizes all available data, including perturbation data (linear response) and the varying operating point (NL response). The proposed approach employs a combined estimator to locally identify the joint LPV‐NL model within the neighborhood of the system's operating point. Although the estimated NL model is localized around this nominal trajectory, an experimental approach is proposed to reduce the linear approximation error, thereby enlarging the validity region of the final model. Finally, we present a numerical example to illustrate the performance of the proposed method.