张玉辉, 姜清辉. 距离最小化数据驱动计算方法中平衡因子取值影响研究[J]. 工程力学, 2022, 39(6): 11-20. DOI: 10.6052/j.issn.1000-4750.2021.03.0199
引用本文: 张玉辉, 姜清辉. 距离最小化数据驱动计算方法中平衡因子取值影响研究[J]. 工程力学, 2022, 39(6): 11-20. DOI: 10.6052/j.issn.1000-4750.2021.03.0199
ZHANG Yu-hui, JIANG Qing-hui. THE INFLUENCE OF THE BALANCE FACTOR IN THE DISTANCE-MINIMIZING DATA-DRIVEN COMPUTATIONAL METHOD[J]. Engineering Mechanics, 2022, 39(6): 11-20. DOI: 10.6052/j.issn.1000-4750.2021.03.0199
Citation: ZHANG Yu-hui, JIANG Qing-hui. THE INFLUENCE OF THE BALANCE FACTOR IN THE DISTANCE-MINIMIZING DATA-DRIVEN COMPUTATIONAL METHOD[J]. Engineering Mechanics, 2022, 39(6): 11-20. DOI: 10.6052/j.issn.1000-4750.2021.03.0199

距离最小化数据驱动计算方法中平衡因子取值影响研究

THE INFLUENCE OF THE BALANCE FACTOR IN THE DISTANCE-MINIMIZING DATA-DRIVEN COMPUTATIONAL METHOD

  • 摘要: 数据驱动计算方法将联立平衡微分方程、几何方程及物理方程的显式求解问题转变为最优化问题,优化目标在于搜索匹配最可能的静力许可应力场、变形许可应变场及应力-应变数据分配方案。在线弹性框架下,探讨了平衡因子取值关于材料常数的量级m和平行偏离程度r对算式收敛速率和性能的影响。结果表明:在松弛问题中,应力可行解和应变可行解关于m的线性收敛比分别为1/(1+m2)和m2/(1+m2),而r的增大则会使二者的收敛速率均降低。分配的数据点在原优化问题中受整型约束的限制,在相邻迭代步间变化率越小,算法早熟收敛现象越显著。r等于0时,数据点在相空间内沿直线路径逼近精确解,在m取1时有着最小的渐进线性收敛比;当r不为0时,数据点的迭代路径不再保持为直线。对于收敛速率较慢的分量,迭代终止时与参考解的偏差幅度增大。精确解附近的数据点密度能够很好保障算法的计算精度,从而降低计算结果对平衡因子取值的敏感性。

     

    Abstract: Data-driven computational methods transform the solution of the simultaneous equations of equilibrium, geometric, and material constitutive laws into an optimization problem. The optimization goal is to search for the best fitted statically-admissible stress field, kinematically-admissible strain field, and stress-strain data assignment. Based on the linear elastic theory, the influence of the magnitude m and the parallel deviation r of the balance factor relative to the material constants on the convergence rate and performance are discussed. The results show that the admissible stress and strain converge linearly at rates of 1/(1+m2) and m2/(1+m2), respectively, in the relaxation problem. Meanwhile, the convergence rates for both the admissible stress and strain decrease with increased r. The assigned data are limited by integral constraints in the original optimization problem, and the low change rate between adjacent iteration steps leads to premature convergence. The stress-strain data approximate the reference solution along a straight path in phase space when r is equal to zero. The gradual linear convergence rate reaches the minimum when m is set to 1. When r is not zero, the iterative path of the data no longer remains a straight line. For the components with a smaller convergence rate, the deviation from the reference solution increases when the iteration stops. The density of the data points near the exact solution provides guaranteed accuracy for the algorithm, thereby reducing the sensitivity of the computational result to the balance factor.

     

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