The Transfer Matrix Metamodel for Dynamic Systems With Arbitrary Time-Variant Inputs
The Transfer Matrix Metamodel for Dynamic Systems With Arbitrary Time-Variant Inputs
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DOI：
10.1115/1.4037630
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发表时间：
2017-10
影响因子：
3.3
通讯作者：
G. Savage;Y. Son
中科院分区：
文献类型：
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作者：
G. Savage;Y. Son
本文讨论的问题，映射的输入变量的向量（对应于离散样本从随时间变化的输入）的输出变量的向量（离散样本的时间相关的响应）。该映射通常由机械模型执行。然而，当机械模型是复杂和动态的时，为了设计目的迭代地生成响应的计算工作量可能是繁重的。元模型（或代理模型）可以是计算效率高的替代品，特别是当输入变量具有某些幅度和频率界限时。在此，从几个训练输入的矩阵和由动态机理模型的模拟提供的匹配响应的对应矩阵创建传递矩阵形式的简单元模型。最小二乘范例揭示了一种将输入矩阵链接到响应矩阵列的简单方法。奇异值分解（SVD）的应用引入了显着的计算优势，因为它提供了矩阵的属性，以优雅的方式，传递矩阵。通过对一个非线性、欠阻尼、双质量弹簧阻尼器系统的研究，证明了传递矩阵的有效性。任意激励和选定的正弦波被施加到检查的准确性，速度和鲁棒性的方法。确定了错误的来源并讨论了减轻错误的方法。与普遍存在的克里格方法相比，传递矩阵方法显示出相似的精度，但大大减少了计算时间。
This paper addresses the problem of mapping a vector of input variables (corresponding to discrete samples from a time-varying input) to a vector of output variables (discrete samples of the time-dependent response). This mapping is typically performed by a mechanistic model. However, when the mechanistic model is complex and dynamic, the computational effort to iteratively generate the response for design purposes can be burdensome. Metamodels (or, surrogate models) can be computationally efficient replacements, especially when the input variables have some amplitude and frequency bounds. Herein, a simple metamodel in the form of a transfer matrix is created from a matrix of a few training inputs and a corresponding matrix of matching responses provided by simulations of the dynamic mechanistic model. A least-squares paradigm reveals a simple way to link the input matrix to the columns of the response matrix. Application of singular value decomposition (SVD) introduces significant computational advantages since it provides matrices whose properties give, in an elegant fashion, the transfer matrix. The efficacy of the transfer matrix is shown through an investigation of a nonlinear, underdamped, double mass–spring–damper system. Arbitrary excitations and selected sinusoids are applied to check accuracy, speed and robustness of the methodology. The sources of errors are identified and ways to mitigate them are discussed. When compared to the ubiquitous Kriging approach, the transfer matrix method shows similar accuracy but much reduced computation time.