# An Intelligent Artificial Neural Network Modeling of a Magnetorheological Elastomer Isolator
###### Abstract  
Recently, magnetorheological elastomer (MRE) has been paid increasingly attention for vibration mitigation devices with the benefits of low power cost, fail safe performances, and fast responses. To make full use of the striking advantages of MRE device, a highly precise model should be developed to predict its dynamic performances. In the work, an MRE isolator in shear-squeeze mixed mode is developed and tested under dynamic loadings. The nonlinear performances in various displacement amplitude and currents are shown. An artificial neural network model with a back-propagation algorithm is proposed to characterize the nonlinear hysteresis of MRE isolator for its implementation in vibration control applications. This model utilized the displacement, velocity, and applied current as inputs and output force as output. The results show that the proposed model has high modeling accuracy and can well portray the complicated behaviors of MRE isolator with different excitations, which shows a fundamental basis for structural vibration control. m m  
To make full use of MRE-based device for vibration mitigation applications, a reliable and accurate model should be developed first for well capturing its nonlinear performances. To date, only a few relative studies have been published. Two main kinds of model are parametric and nonparametric model [11]. The parametric model includes several elements (e.g., spring, dashpot, slippery element, and hysteresis element) with physical meanings for describing the force-displacement curves [6; 12; 13; 14; 15], which is phenomenon model for better explaining the nonlinear performances of MRE-based devices. However, for parametric models, complicated parameter identification processes cannot be avoided. In some cases, the identified parameters are negative which is unrealistic for parametric modeling. Additionally, some parametric models (e.g., Bouc-Wen model, hyperbolic model, LuGre model) including nonlinear differential equations, which may bring the inconvenience for implementation of feasible controller design [16]. Compared with parametric models, nonparametric models may establish nonlinear force-displacement loops without parameter identifications, and has high accuracy and adaptability [16]. It is noted that the non-parametric model is not able to be solved by a mathematical model, and hence unrealistic parameters sometimes arise in parametric modeling method may be not existing. Nonparametric model is mainly based on artificial intelligence methods, in which neural network model is one of the most typical models. By neural network nonparametric model, the input and output responses are linked by mapping structure. Based on the training process, a neural network model could portray nonlinear relationships between loading conditions and output control force of MRE-based device, which has advantages of fast convergence and precision. However, only a few studies have been reported on this issue [16; 17]. In this work, for improving adaptability and reducing complexity of neural network nonparametric modeling, a back-propagation artificial neural network (BPANN) structure is utilized for modeling MRE isolator. BPANN model is a feed-forward neural network using an algorithm of error reverse transfer training. This model has several hidden layers between input layers and output layers, and makes the mapping results approximately to the output force of MRE isolator by adjusting the weight of the neural network. The detailed organization of the paper is presented as follows. Section 2 introduces the design and working principle of MRE isolator. A series of experimental tests for characterizing MRE-based device are conducted under various dynamic loadings in Section 3. Field-dependent and displacement amplitude-related force-displacement loops are observed. In Section 4, a BPANN model is developed and utilized for capturing nonlinear hysteresis loops of MRE isolator. The comparison of predicted results and experimental results is discussed.