Hysteretic Systems Research Articles

Robust control of uncertain asymmetric hysteretic nonlinear systems with adaptive neural network disturbance observer

Robust control of uncertain asymmetric hysteretic nonlinear systems with adaptive neural network disturbance observer

Adaptive Neural Control for Hysteretic Nonlinear Systems With Hysteresis Neural Direct Inverse Compensator and Its Application.

Aiming at high precision control for a class of hysteretic nonlinear systems, a new hysteresis direct inverse compensator-based adaptive output feedback control scheme is designed in this article. First, a novel long short-term memory neural network (LSTMNN)-based hysteresis inverse compensator is established to compensate the asymmetric hysteresis nonlinearity, where the LSTMNN is used as the prediction mechanism for model operator weights, rather than the overall mapping of hysteresis input and output. Second, by designing the modified high-gain K-Filter states observer and the error transformed function, the unmeasurable states are estimated with arbitrarily small estimation error and the prespecified tracking performance is achieved. Lastly, the biconical dielectric elastomer actuator (DEA) motion platform is constructed. Then, the effectiveness of the proposed LSTMNN-based hysteresis inverse compensator and control scheme are verified on the experimental platform. The experimental results illustrate the effectiveness and advantages of proposed control scheme.

Inversion-based fuzzy adaptive control with prespecifiable tracking accuracy for uncertain hysteretic systems

Inversion-based control strategies have the outstanding effectiveness in the compensation for hysteresis nonlinearities. However, when the plant is driven by smart material-based actuator with the information absence of hysteresis output, there still exist technical gaps in the construction of hysteresis inverse controller. Therefore, this study aims to address this gap by proposing a novel control scheme. Technically, a novel hysteresis inverse algorithm, significantly reducing computational burden, has been proposed based on a novel adaptive estimation method for the unknown parameter (density function) in the Preisach-typed hysteresis nonlinearity. Furthermore, the inverse compensation error, the nonlinearities and uncertainties appeared in the controlled plant are accommodated by the innovative adaptive fuzzy feedback controller. With our scheme, it can ensure that the closed-loop stability, predefined steady-stated tracking performance and the convergence of algorithms including inverse algorithm and adaptive updating laws. In addition to theoretical analysis, we have validated the effectiveness of the proposed control scheme through simulation comparisons and experimental results conducted by the real-life piezoelectric actuator.

Survival probability surfaces of hysteretic fractional order structures exposed to non-stationary code-compliant stochastic seismic excitation

A novel first-passage probability stochastic incremental dynamics analysis (SIDA) methodology tailored for hysteretic fractional order structural systems under a fully non-stationary seismic excitation vector consistently designated with contemporary aseismic codes provisions (e.g., Eurocode 8) is developed. Specifically, the vector of the imposed seismic excitations is characterised by evolutionary power spectra that stochastically align with aseismic codes elastic response acceleration spectra, defined for specified modal damping ratios and scaled ground accelerations. Leveraging the concepts of stochastic averaging and statistical linearization, the approximative non-stationary response displacement joint probability density function (PDF) is derived, retaining the particularly coveted attribute of computational efficacy. Subsequently, the coupling with the survival probability model allows for the efficient determination of the response first-passage time probability density surfaces and the survival probability surfaces across various limit-state rules and scalable intensity measures. The first-passage time probability serves as a robust engineering demand parameter, effectively monitoring structural behaviour by considering both intensity and timing information, while inherently aligned with pertinent limit-state requirements. Notably, the associated low computational cost and the ability to handle a wide range of complex nonlinear/hysteretic structural behaviours, coupled with its compliance with modern aseismic codes, underscore its potential for applications in the fields of structural and earthquake engineering. A nonlinear system endowed with fractional derivative elements is used to exemplify the method’s reliability. The accuracy of the proposed method is validated in a Monte Carlo-based context, conducting nonlinear response time–history analyses with an extensive ensemble of accelerograms compatible with Eurocode 8 response acceleration spectra.

A bi-fidelity DeepONet approach for modeling hysteretic systems under uncertainty

This study proposes a multi-fidelity paradigm for developing surrogates of degrading hysteretic systems under uncertainty through the use of deep operator networks (DeepONets). Instead of attempting to directly train a DeepONet on the original response, this study adopts a residual modeling approach wherein the DeepONet is trained on the discrepancy between the original (high-fidelity) data source and a relatively simpler (low-fidelity) representation of the system. Within these examples, a conventional Bouc-Wen model is treated as a “low-fidelity” representation given that it is free of any further assumptions about the nonlinear behavior, while the “high-fidelity” data is generated from different structures with various forms of complex hysteretic behavior. The results of this study show that the proposed multi-fidelity approach consistently outperforms standard surrogates trained on only the original datasets considering a variety of systems with unknown parameters. The results also show that the difference in performance grows as training data becomes more scarce, a critical consideration for many real-world engineering systems, and that the proposed multi-fidelity approach maintains its performance edge even when controlling for training time and noise in the training data.

A novel LSTM-integrated non-intrusive ROM for reliability analysis of hysteretic systems with large stochastic dimension

Failure probability estimation of hysteretic systems subjected to random process excitation appears in many practical engineering applications, such as structures subjected to earthquake and vibration control. This task is computationally challenging due to the need for repeated solutions of a high-resolution model. This cost grows significantly with the stochastic dimension — characterized by the number of random variables, in this case, arising from the discretization of the random excitation. To address this issue, a novel non-intrusive reduced order model (ROM) is proposed in this paper. Accordingly, the complexity due to spatial discretization is first reduced using proper orthogonal decomposition. However, interpolation among response time histories in the resulting reduced solution space is computationally infeasible due to large stochastic dimensionality. An existing ROM developed by the authors is now improved by adopting a long short-term memory (LSTM) network for this interpolation. Furthermore, this adoption required two additional modifications in the mathematical structure of the ROM related to data compression and nonlinear coupling. The proposed methodology can be seamlessly integrated with black-box nonlinear solvers. Through detailed numerical studies on a beam on Winkler foundation and a multi-storied building frame subjected to stationary and non-stationary excitations, the proposed ROM is found to be accurate, efficient, and robust with respect to the frequency band of interest. The ROM has shown reduction of two orders of magnitude in the computational time. Furthermore, the proposed ROM is inherently parallelizable and holds promise to be scaled to other types of nonlinear systems with large stochastic dimensionality.

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Stochastic response of chain-like hysteretic MDOF systems endowed with fractional derivative elements and subjected to combined stochastic and periodic excitation

Stochastic response of chain-like hysteretic MDOF systems endowed with fractional derivative elements and subjected to combined stochastic and periodic excitation

Hysteretic models with damage and flexibility increase

The need to accurately describe nonlinear degrading phenomena in both modern and classical complex materials that exhibit hysteretic behavior is a relevant task for the analysis of their response. In the present study an enrichment to an existing formulation to describe strength and stiffness degradation is proposed. The description of damage, that reduces the hysteretic force, is then accompanied by the introduction of flexibility increase, which increments the elastic displacement experienced by the system. Both effects influence the energy dissipated by the system. The condition of thermodynamic admissibility in presence of damage and flexibility increase is derived, entailing constraints on system parameters. Additional constraints arise from consistency conditions on the transformation of the pure hysteretic system into the system with damage and flexibility increase. A numerical solution involving the forward Euler method is presented to evaluate the response quantities. The formulation is eventually applied to the elastic–plastic and Bouc Wen hysteresis models, and the influence of the degrading parameters is presented. The presented Bouc-Wen model with damage and flexibility increase is applied to study the cyclic response of a masonry panel experimentally tested to validate the numerical model and prove its capability of describing the structural response.

Decentralized Implicit Inverse Control for Large-Scale Hysteretic Nonlinear Time-Delay Systems and Its Application on Triple-Axis Giant Magnetostrictive Actuators.

This article proposes fuzzy-logic systems (FLSs)-based decentralized adaptive implicit inverse control scheme for a class of large-scale nonlinear systems with time delays and multihysteretic loops. Our novel algorithms feature hysteretic implicit inverse compensators designed to effectively mitigate multihysteretic loops in large-scale systems. In this article, hysteretic implicit inverse compensators can replace the traditional hysteretic inverse models, which are exceedingly difficult to construct, and no longer necessary. The authors provide three contributions: 1) a searching mechanism to obtain the approximate value of the practical input signal from the so-called hysteretic temporary control law; 2) the arbitrarily small L∞ norm of the tracking error attained by utilizing the proposed initializing technique, which applies the combination of FLSs and a finite covering lemma to deal with time delays; and 3) the construction of a triple-axis giant magnetostrictive motion control platform, which validates the effectiveness of the proposed control scheme and algorithms.

Reliability control of nonlinear stochastic dynamical system based on discrete data

Stochastic optimal control based on reliability plays a crucial role in mitigating structural failure and ensuring safe operation. For general stochastic vibration systems, a data-driven method for reliability-based optimal control is proposed based on random state data. Firstly, the feedback control is split into conservative and dissipative components in coherence with physical intuition, and each component is expanded upon using pre-selected basic functions, resulting in a modified system with undetermined coefficients. Then, from discrete random samples, the expressions for the probability densities of the first-passage time and the stationary response can be identified, explicitly including system and excitation parameters, as well as initial and safety boundary conditions. Finally, a performance index, combining system reliability and control cost, is constructed and can be explicitly expressed in terms of the undetermined coefficients of the control forces. The optimal control problem for determining the optimal control forces is reformulated as an optimization problem for determining the coefficients that minimize the performance index. This unconstrained optimization problem can be easily solved. Three typical nonlinear stochastic systems, a controlled Duffing oscillator, a controlled nonlinear hysteretic system, and a controlled 2-DOF nonlinear dynamical system, are given to illustrate the validity and accuracy of the proposed data-driven method. Additionally, the control performance of the optimal control strategy in improving the system reliability is also discussed.

Model-free compensation learning control of asymmetric hysteretic systems with initial state learning

In this article, a model-free compensation learning control scheme is presented for asymmetric hysteretic systems to achieve high-precision output tracking, where the effects of asymmetric input hysteresis nonlinearities are denoted by the asymmetric Prandtl–Ishlinskii model (APIM). In the presented control scheme, the feedforward iterative learning technique is generalized to the control design of asymmetric hysteretic systems. To improve the robustness and dynamic performance of the existing feedforward learning control for hysteretic systems, both the feedback action and the differential term are utilized to design a discrete-time PD-P open-closed-loop learning control law for simultaneously compensating the asymmetric input hysteresis nonlinearities and the linear dynamics effects without constructing compensators based on their models. The initial state error of such a system is also considered, a modified initial state learning strategy is proposed to ensure the initial state error tends to a prescribed level with the increasing of iterations. By fully analyzing the properties of the APIM, the convergence conditions with respect to the input error, the state error, and the tracking error along the iteration domain are given. The simulation and experimental results are provided to demonstrate strong robustness and excellent tracking accuracy with the proposed model-free compensation learning control scheme.

Phản ứng động đất của các hệ nhị tuyến tính đàn - dẻo và tự tâm định dưới tác dụng của các chuyển động nền do động đất xa và gần

This study presents seismic response of single degree of freedom (SDOF) elasto-plastic and self-centering systems under far and near-fault ground motions. These parameters was conducted to determine the influence on SDOF structure response in term of ductility, absolute acceleration, absorbed energy, strength ratio and strength reduction factor. It was found that maximum ductility for bilinear elasto-plastic systems was qualitatively similar to self-centering hysteretic systems, by adjusting the value of α and β, a self-centering hysteretic systems could be made qualitatively better than bilinear elasto-plastic systems in term of ductility. With respect to the absorbed energy, the self-centering hysteretic systems always less than comparable bilinear elasto-plastic systems. A three 3-story steel frame Self-Centering Brace Frame (SCBF) was designed according AISC seismic provison to validate of response of single degree of freedom self centering systems. 20 far field earthquake groundmotion are used for analysing of three 3-story steel frame SCBF under DBE (Design Based Earthquake) and MCE (Maximum Considerded Earthquake) level by using computer program PISA3D. The maxmimun value of interstory drift are under 1% and 2%, while residual drift are small.

Frequency-response curves for rate-independent hysteretic mechanical responses of complex shape

We illustrate the performances of a brand new hysteretic model, recently proposed and denominated VRM+D, to characterize the nonlinear response of mechanical systems endowed with quite complex hysteretic behaviors. To this end, we combine the VRM+D with a continuation procedure based on Poincaré maps developed by Lacarbonara et al. in 1999. In this way, the steady-state response, as well as stability and bifurcation, of a large class of mechanical systems can be analyzed. In particular, we show the effectiveness of the VRM+D, in conjunction with the Poincaré map-based continuation procedure, in accurately predicting periodic solutions of the above-mentioned systems independently of the form of the hysteresis loop shapes. Furthermore, we draw some general considerations on the potential applications of the proposed approach in different fields of engineering to get an improved understanding of the dynamics of hysteretic mechanical systems subjected to cyclic loading.

Adaptive Neural Indirect Inverse Control for a Class of Fractional-Order Hysteretic Nonlinear Time-Delay Systems and Its Application

Adaptive Neural Indirect Inverse Control for a Class of Fractional-Order Hysteretic Nonlinear Time-Delay Systems and Its Application

Output Feedback Bounded Control for Unidirectional Input Constrained Hysteretic Systems With Application to Piezoelectric-Driven Micropositioning Stage

Output Feedback Bounded Control for Unidirectional Input Constrained Hysteretic Systems With Application to Piezoelectric-Driven Micropositioning Stage

Understanding Effects of Evolutionary Arias Intensity on Nonlinear Behavior of Hysteretic Systems and Liquefiable Grounds

ABSTRACT The effects of evolutionary Arias intensity are thoroughly investigated based on ground motion simulation and nonlinear dynamic response. A new methodology is developed to generate a series of spectral-equivalent synthetic motions with different energy accumulation paths using wavelet packets. Systematic studies are performed on dynamic responses of hysteretic systems and liquefiable grounds using the simulated motions and actual recordings. An attempt is made to develop the relationship between liquefaction-induced deformation and shaking intensity rate which is used to quantify the rate of Arias intensity accumulation. The results indicate the need of considering evolutionary Arias intensity in nonlinear dynamic analysis.

Disturbance observer-based robust optimal control of rate-dependent hysteretic systems: Application to a piezoelectric nano-manipulator

This article investigates the robust and optimal control problem of hysteretic systems with both parameter variations and unmodeled dynamics. By means of a hysteresis compensator based on a modified Prandtl–Ishlinskii model and a feedback controller, a novel robust optimal control architecture is proposed to address the asymmetric and rate-dependent hysteresis nonlinearities and various disturbances, where the compensation errors, parameter variations, and unmodeled dynamics are treated as a bounded disturbance. The proposed controller is composed of two components: a high order sliding mode observer and an extended linear quadratic controller. The high order sliding mode observer is introduced to guarantee that the disturbance observation error converges to the origin in a finite time such that the extended linear quadratic controller enables the predefined optimal performance to be achieved. Moreover, the exponential stability of the closed-loop system has been proven, and some sufficient conditions are given. Finally, the proposed control algorithm is applied to a piezoelectric nano-manipulator system, both the good hysteresis modeling accuracy and excellent tracking performance are demonstrated in the real-time experiments.

Identification of structured nonlinear state–space models for hysteretic systems using neural network hysteresis operators

Hysteretic system behavior is ubiquitous in science and engineering fields including measurement systems and applications. In this paper, we put forth a nonlinear state–space system identification method that combines the state–space equations to capture the system dynamics with a compact and exact artificial neural network (ANN) representation of the classical Prandtl–Ishlinskii (PI) hysteresis. These ANN representations called PI hysteresis operator neurons employ recurrent ANNs with classical activation functions, and thus can be trained with classical neural network learning algorithms. The structured nonlinear state–space model class proposed in this paper, for the first time, offers a flexible interconnection of PI hysteresis operators with a linear state–space model through a linear fractional representation. This results in a comprehensive and flexible model structure. The performance is validated both on numerical simulation and on measurement data.

Dynamic behavior analysis of systems with friction and hysteretic effects

This paper investigates the steady-state response of a nonlinear system that incorporates both a hysteretic element and frictional contact under harmonic excitation. While previous studies have separately explored hysteretic oscillators and frictional systems, the simultaneous consideration of both elements has received limited attention. In this study, an analytical solution for the steady-state response is proposed, employing the equivalent linearization approach. This method enables the determination of equivalent stiffness and equivalent damping coefficients for the linearized system, which are directly linked to the amplitude of the steady-state response. To validate the derived analytical solution, a numerical model is utilized, demonstrating the agreement between the analytical and numerical results. Moreover, this paper identifies noteworthy dynamic characteristics of the designed system, notably the occurrence of peak amplitude at excitation frequencies lower than the pre-yield natural frequency. Furthermore, the apex point can be adjusted by manipulating the nonlinear parameters. Building upon these observations, a new mounting system is examined, revealing distinctive behavior.