Estimating the forcing function in a mechanical system by an inverse calibration method
Estimating the forcing function in a mechanical system by an inverse calibration method
复制标题
DOI：
10.1177/10775463211031053
复制
发表时间：
2021-07
影响因子：
2.8
通讯作者：
C. Rice;J. Frankel
中科院分区：
文献类型：
--
作者：
C. Rice;J. Frankel
本文提出并演示了一种基于校准的积分公式，用于在给定位移或加速度数据的情况下求解质量-弹簧-阻尼器系统中的力函数。所提出的方法在振动方面是新颖的，并在传热领域进行了深入研究。当通过恒定属性、线性、时不变常微分方程系统进行数学描述时，该方法可以进一步扩展和推广到与机器零件、车辆悬架、平移和旋转系统、齿轮系统等相关的多变量系统。力函数的解析方法和随后的数值重建基于求解运动方程的无参数反演公式。校准方法在频域中制定，并利用降维产生的多个观察结果，形成涉及输入输出关系和拥有所有系统参数的传递函数的代数系统。从校准工作中消除了传递函数代替实验数据，从而减少了系统误差。这些无参数、减少系统误差的方面是所提出方法的独特且新颖的优点。形成仅包含未知的力函数和实验数据的第一类Volterra积分方程。与所有不适定问题一样，必须引入正则化来稳定系统。建立了一种未来技术，用于根据所选的正则化参数形成一系列预测。结合相平面分析和互相关原理来估计最佳正则化参数。最后，进行数值模拟验证所提出的方法。
This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.