Bouc-Wen Hysteretic Model Research Articles

A radial torsional coupled two-axis bushing model based on Bouc-Wen hysteretic model

For the case when radial deformation and torsional deformation are exerted simulatenously, a radial?torsional coupled two-axes bushing model based on the Bouc-Wen hysteretic model is suggested. Bushing is tested to capture the nonlinear behaviour of the bushing according to the displacement and frequencies using a MTS machine. A modified Bouc-Wen model and standard solid model are combined to represent the nonlinear responses due to excitations with several amplitudes and frequencies. The sensitivity analysis is carried out to identify the parameters of the proposed model. Simulation results are compared to test results for verification.

VERIFICATION OF IDENTIFICATION METHOD FOR NONLINEAR HYSTERETIC SYSTEMS UTILIZING SHAKING TABLE TESTS OF FULL-SCALE 4-STORY STEEL BUILDING

The already proposed identification method for nonlinear hysteretic systems is applied to shaking table tests of a full-scale 4-story steel building at the E-Defense. The structure is modeled as a 4DOF nonlinear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as the Bouc-Wen hysteretic model. The identified hysteretic curve is compared to the corresponding experimental result.

Structural health monitoring using adaptive LMS filters

A structure's level of damage is determined using a non-linear model-based method utilizing a Bouc-Wen hysteretic model. It employs adaptive least mean squares (LMS) filtering theory in real time to identify changes in stiffness due to modeling error damage, as well as permanent displacements, which are critical to determining ongoing safety and use. The structural health monitoring (SHM) method is validated on a 4-story shear structure model undergoing seismic excitation with 10% uniform noise added. The method identifies stiffness changes within 0.5-1.0% inside 0.2-1.0 seconds at different sampling frequencies. Permanent deflections are identified to within 10% of the true value in 1.0 second, converging further over the remainder of the record.

Lifecycle cost–benefit analysis of isolated buildings

Seismic isolation is effective in reducing seismic demand to buildings and mitigating seismic damage costs. To corroborate this fact quantitatively by taking all possible seismic events that occur during the service period of a building into account, this study investigates probabilistic characteristics of the peak ductility demand of inelastic superstructures with linear/bilinear base isolators subject to hundreds of strong ground motion records, and then assesses the cost-effectiveness of seismic isolation technology from the lifecycle cost–benefit perspective. Based on results from nonlinear dynamic analyses of two-degree-of-freedom systems with the Bouc–Wen hysteretic model, a prediction model for the peak ductility demand of isolated structures is developed and used in lifecycle cost analysis to assess the cost-effectiveness of seismic isolation systems. The analysis results show that seismic isolation reduces vibration in superstructures significantly and can be cost-effective in mitigating seismic risk.

Genetic-Algorithm-Based Strategies for Dynamic Identification of Nonlinear Systems with Noise-Corrupted Response

The main objective of this paper is to investigate efficiency and correctness of different real-coded genetic algorithms and identification criteria in nonlinear system identification within the framework of non-classical identification techniques. Two conventional genetic algorithms have been used, standard genetic algorithm and microgenetic algorithm. Moreover, an advanced multispecies genetic algorithm has been proposed: it combines an adaptive rebirth operator, a migration strategy, and a search space reduction technique. Initially, a critical analysis has been conducted on these soft computing strategies to provide some guidelines for similar engineering and physical applications. Therefore, the hysteretic Bouc-Wen model has been numerically investigated to achieve three main results. First, the computational effectiveness and accuracy of the proposed strategy are checked to show that the proposed optimizer outperforms the aforementioned conventional genetic algorithms. Secondarily, a comparative study is performed to show that an improved performance can be obtained by using the Hilbert transform-based acceleration envelope as objective function in the optimization problem (instead of the pure acceleration response). Finally, system identification is conducted by making use of the proposed optimizer to verify its substantial noise-insensitive property also in the presence of high noise-to-signal ratio.

Reliability Analysis of Uncertain Nonlinear System Subject to Correlated Failure

On the basis of the Bouc-Wen hysteretic model, a numerical method for the reliability analysis of stochastic multi-degree-of-freedom hysteretic system with correlated failure modes is presented. Under the first passage model, considering the random caused by hysteretic loop itself, the theory of incomplete probability information and the fourth-moment technique and Gram Charlier series are employed to develop a numerical reliability analysis method systematically. The numerical example reveals that in most of cases, though system is characterized by a set of independent random parameters, the responses are strongly correlated, and correlation coefficient between the responses is fluctuated with time. The system reliability with correlated failure modes is evaluated with proposed method, and the result obtained by this method is compared well with the Monte-Carlo simulations.

New nonlinear bushing model for general excitations using Bouc-Wen hysteretic model

Because the characteristics of rubber bushing significantly affect the accuracy of vehicle dynamics simulations, they should be accurately modeled in the vehicle suspension model. In this paper, a new nonlinear bushing model for automotive bushing components is developed to improve the accuracy of vehicle dynamics analysis. Bushing components were first tested to capture the nonlinear and hysteretic behavior of typical elements by using a MTS 3-axis elastomer tester. A simple Bouc-Wen hysteretic differential model was modified to generate a more precise rubber bushing model. A sine wave, step input, and random excitations are imposed on the bushing. The ADAMS program is used to calculate sensitivity and the VisualDOC program is employed to find the optimal parameters for the bushing model. An error function is designed to find optimal parameters of the model. Parameter identification is carried out to satisfy the static and dynamic characteristics due to sine and step excitation inputs. It was proved that the proposed model could predict the bushing forces under sine, step, and random inputs well. The errors are within 10% in the overall range. To show the validity of the proposed model, a numerical example was also carried out. Because the bushing forces due to random excitation input show good agreement with experiments, the proposed bushing model is available in the vehicle dynamics simulation.

On the response and dissipated energy of Bouc–Wen hysteretic model

An efficient formulation for the response and dissipated energy of Bouc–Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss’ hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems.

Hysteretic Property of Rare Earth Giant Magnetostrictive Actuator

Based on the hysteretic theory of the giant magnetostrictive material (RE-GMM) and the nonlinear characteristic of the giant magnetostrictive actuator (GMA), the composite nonlinear mathematic model was established with Bouc-Wen hysteretic model, and the hysteresis properties and the hysteresis loop of the transducer were investigated. Then with Multi-scale method, the analytic solution of the response and the expression of the frequency-response properties, which the giant magnetostrictive actuator with hysteretic and geometric nonlinear vibration characteristic included, were achieved, and the t-x curve was obtained. Then, after the discussing about the different cases, the frequency-response curves were obtained with damp case and without damp case, and the affect of frequency-response characteristic with damp expressed by the dynamic excitation f, piezomagnetic coefficient d 33 and magnetic conductivity μ33 T to the curve of the frequency-response is discussed. Results indicated that the effect of f, d 33 and μ33 T to the amplitude and nonlinear of the system was obvious. At the same time, the frequency-response curve had the phenomenon of double hopping.

Stochastic energy analysis of seismic isolated bridges

In this paper, a parametric stochastic analysis of isolated bridge is proposed with the aim to assess isolation performance and to investigate effects of energetic influence on protection efficiency. The analysis has been carried out in terms of two stochastic parameters of pear-deck maximum displacement and hysteretic energy response, of which a qualitative trend has been observed. Isolated bridge is described by a simple two degree of freedom (TDoF) Bouc–Wen hysteretic model, which has been introduced for its intrinsic ability in reproducing a wide range of real devices behavior. With the aim of taking into consideration intrinsic stochastic nature of seismic events, the ground motion and the structural response have been described by random vibration approach. Results obtained show that protection achieved by shifting structural natural period and reducing input energy by devices dissipation have counteracting effects if related to deck lateral displacement.

Comparison of semi-physical and black-box bushing model for vehicle dynamics simulation

Since bushing components have highly nonlinear characteristics according to the amplitude and the frequency, it is hard to derive a mathematical modeling of the bushing. In this paper, a semi-physical bushing model and a black-box bushing model are derived and compared. A Bouc-Wen hysteretic model is employed to derive a semi-physical model and an artificial neural network algorithm is used to make a black-box bushing model. A 3-axes MTS rubber test machine is used to capture the bushing characteristics. Sine excitation tests based on the different frequencies and different amplitudes are performed to find out the bushing characteristics. Random test results are also used to generate the coefficients of a semi-physical model and weighting factors of the black-box model. Random simulations are carried out to verify the bushing models and the results are compared with each other according to the numerical efficiency and accuracy.

On the Hysteretic Bouc–Wen Model

This paper deals with the problem of identifying the parameters of the hysteretic Bouc–Wen model. In the existing literature, the methods devoted to this problem rely mainly on numerical simulations and do not have, to a very large extent, a rigorous mathematical justification. Our method consists in exciting the hysteretic system with a periodic input and obtain the desired parameters from the resulting limit cycle. The identification method that we propose has a rigorous mathematical basis as it based on the analytic description of the limit cycle, and, unlike existing identification methods for the Bouc–Wen model, gives guaranteed relative errors between the (unknown) exact model parameters and their corresponding estimates. We also prove that this method is robust with respect to constant and T-periodic disturbances commonly present in any laboratory experiment. A numerical simulation example illustrates the use of our identification method.

Analytical and Experimental Study of the Response of a Suspension System with a Magnetorheological Damper

A single-degree-of-freedom suspension system with a magnetorheological (MR) damper is studied. A Bouc-Wen hysteretic model is adopted to represent the nonlinear hysteretic damping force of an MR damper. The model parameter identification process is carried out based on the experimental data. The equivalent linearization and the averaging methods are employed to simplify the hysteretic nonlinear model of the system, and to obtain the system response under sinusoidal base excitation. The results obtained by these two approximate methods are compared with the results obtained from the experiments and the numerical simulation method when a swept sine excitation with amplitudes of 0.5 and 0.75 mm is applied to the system. The comparison shows that the results obtained by the equivalent linearization method and the averaging method are very similar and have a good agreement with both the experimental and the numerical results. Moreover, the effects of the hysteretic model parameters are investigated after the system dynamical equations are nondimensionalized.

PHYSICAL CONSISTENCY OF THE HYSTERETIC BOUC-WEN MODEL

This paper deals with the determination of the conditions for which the hysteretic Bouc-Wen model is consistent with the physical phenomenon it is supposed to represent. In particular, we derive the conditions on the model parameters under which the model is stable, asymptotically dissipative and verifies the hysteretic property. These conditions are in the form of algebraic inequalities to be verified by the Bouc-Wen model parameters.

Stochastic Optimal Semi-Active Control of Nonlinear Systems by Using MR Dampers

A stochastic optimal semi-active control strategy for strongly nonlinear oscillator subjected to external and/or parametric excitations of Gaussian white noises using magneto-rheological (MR) damper is proposed. The dynamic behavior of an MR damper is characterized by using the Bouc-Wen hysteretic model. The control force produced by the MR damper is split into a passive part and a semi-active part. The passive part is incorporated with the uncontrolled system to form a passive control system. Then the system is converted into an equivalent nonlinear non-hysteretic stochastic control system, from which an Itô stochastic differential equation for total energy is derived by using the stochastic averaging method of energy envelope. For the ergodic control problem, a dynamical programming equation for the controlled total energy process is established based on the stochastic dynamical programming principle. The optimal control law is obtained by minimizing the dynamical programming equation and can be implemented by the MR damper without clipping. Then the fully averaged Itô equation for the controlled total energy process is obtained by replacing the control force with the optimal control force and completing the averaging. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. The efficacy of the proposed stochastic optimal semi-active control strategy is illustrated by using the numerical results for two examples.

On‐line identification and damage detection in non‐linear structural systems using a variable forgetting factor approach

AbstractThis paper presents an adaptive on‐line identification algorithm based on a newly defined variable forgetting factor approach. At each time step, the proposed methodology, a recursive least‐square (Kalman filter) based algorithm, upgrades the adaptation gain matrix using an adaptive forgetting factor that is expressed as the ratio between the minimum value of the diagonal elements of the adaptation gain matrix and a set of pre‐defined threshold values. This approach requires only acceleration measurements and is particularly robust to the integration errors introduced in determining velocities and displacements. Such an algorithm has been implemented for both parametric and non‐parametric identification studies. For the case of no a priori information on the type of the structural model, an analytical method based on a power series of multivariable polynomial expansions has been introduced. The effectiveness and robustness of the proposed approach has been shown in various numerical simulations, considering the effects of excitation amplitude, of measurement noise, of a priori mass estimation error, and of exact‐, under‐, and over‐parameterization of the structural model. General polynomial‐type non‐linear models such as Duffing and Van der Pole oscillators and Bouc–Wen hysteretic model have been analyzed using the proposed modeling process. The methodology presented in this paper leads to a more accurate and controllable on‐line identification either for the estimation of time‐invariant or time‐varying structural parameters (for damage detection purposes) or for the prediction of the future structural response to dynamic loading. Copyright © 2003 John Wiley & Sons, Ltd.

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined. The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters. Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.

Dynamic analysis method of a combined energy dissipation system and its experimental verification

AbstractA combined energy dissipation system is developed in this paper. In this system lead rubber dampers and their parallel connection with oil dampers are used in the braces of a structural frame. A dynamic analysis method of the system, including the modelling of the lead rubber damper and the oil damper, is proposed. In the analysis method, the restoring force characterestics of the lead rubber damper is simulated by the Bouc–Wen hysteretic model, and the behaviour of the oil damper is simulated by a velocity and displacement‐related model in which the contributions of the oil damper to the damping force and stiffness of the system are considered. A series of shaking table tests of a three‐storey steel frame with the combined energy dissipation system are carried out to evaluate the performance of the system and to verify the analysis method. The test and analysis show that the performance of the combined energy dissipation system is quite satisfactory and there is a good agreement between the analysis and test results, which indicates that the analysis method proposed in this paper is valid and suitable for the dynamic analysis of the combined energy dissipation system. Copyright © 2002 John Wiley & Sons, Ltd.

Equivalent linearization of the Bouc–Wen hysteretic model

The smooth endochronic hysteretic Bouc–Wen model is studied from the point of view of random vibration. The sources of the errors of the method of equivalent linearization applied to this model using the hypothesis of joint Gaussian behaviour are examined. The method of linearization for softening hysteretic models proposed by the authors, which is based on a combination of Dirac and Gauss densities, is developed and applied to the Bouc–Wen model under a variety of conditions. It is shown that the method gives excellent estimations of the response statistics without increasing the computational effort required by the conventional technique.

Parameter identification for degrading and pinched hysteretic structural concrete systems

Hysteretic models are frequently used to predict the non-linear behavior of reinforced concrete structural systems. Such models are typically characterized by control parameters that have to be calibrated from observed experimental testing. A system identification methodology is presented in this paper for determining the values of control parameters in a continuously smooth hysteretic model for inelastic dynamic behavior of structural concrete systems. The technique is based on a modified Gauss-Newton approach in which a non-linear relationship between model parameters and the force-deformation or moment-curvature hysteretic loops is assumed. The methodology is applied to an extended version of the well known rate-dependent Bouc-Wen hysteretic model. Six control parameters are introduced into the model which influence the degrading characteristics and, therefore, represent the target parameters that need to be optimized. The versatility of the approach is demonstrated through sample simulations of observed behavior which are drawn from reinforced and partially prestressed concrete elements and subassemblages including beams, columns and beam-column joints. Studies of convergence of the proposed algorithm and sensitivity of the model to identified parameters is presented.