分数阶黏弹性振子系统响应的代理模型分析

粘弹性缓冲系统由于其具有较高的振动耗散能力，已被广泛应用于车辆阻尼减振。针对分数阶模型描述粘弹性缓冲系统力学特性时存在的复杂度高、难以直接进行参数优化等问题，引入代理模型减少优化时的计算复杂度。首先，通过分数阶建模给出一种用于阻尼减振的分数阶粘弹性缓冲系统。其次，依据分数阶导数算子定义间的关系推导出分数阶微分算子的一种差分格式，用于求解该系统的数值响应，并对系统参数灵敏度进行分析；最后，选用灵敏度较高的系统参数作为优化变量，选用Kriging模型和二次响应面模型对系统的响应函数进行代理。结果表明：相对于Kriging模型，二次响应面代理模型能够在较少样本点时达到较高的精度。该研究可为分数阶粘弹性振子系统响应分析及工程设计提供理论参考。

Surrogate Model Analysis of Response of Fractional Viscoelastic Oscillator

Viscoelastic buffer system has been widely used in vehicle damping because of its high vibration dissipation ability. In order to solve the problems of high complexity and difficulty in parameter optimization when describing the mechanical properties of viscoelastic buffer system with fractional order model, a surrogate model is introduced to reduce the computational complexity of optimization. Firstly, a fractional viscoelastic buffer system for damping is presented by fractional modeling. Secondly, according to the relationship between the definitions of fractional derivative operators, a difference scheme of fractional derivative operators is derived, which is used to solve the numerical response of the system, and the sensitivity of system parameters is analyzed. Finally, the system parameters with high sensitivity were selected as the optimization variables, and the Kriging model and the quadratic response surface model were used to proxy the response function of the system. The results show that compared with the Kriging model, the quadratic response surface surrogate model can achieve higher accuracy with fewer sample points. This study can provide theoretical reference for response analysis and engineering design of fractional viscoelastic vibration subsystem.