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A novel interval model updating framework based on correlation propagation and matrix-similarity method
Mechanical Systems and Signal Processing ( IF 8.4 ) Pub Date : 2021-05-23 , DOI: 10.1016/j.ymssp.2021.108039
Baopeng Liao , Rui Zhao , Kaiping Yu , Chaoran Liu

Model updating techniques have achieved extensive applications in numerical models with uncertainties inherently in practical systems, whereas the stochastic theory is ineffective under insufficient knowledge. Additionally, model updating in the face of correlated uncertainties and complex numerical models remains challenging. In the present study, a novel interval model updating framework was proposed to tackle down the correlated uncertainties with limit samples. Such a framework has the advantage that parameters can be updated with high precision regardless of whether the relationship between input and output is linear or nonlinear. To achieve this advantage, the convex modelling technique and the Chebyshev surrogate model were employed for uncertain parameter quantization and numerical model approximation, respectively. Subsequently, the matrix-similarity method considering correlation propagation was developed to build the two-step interval model updating process, which was converted into a deterministic model updating problem. The mentioned process simplified the model complexity, while improving the accuracy of the updated results. Notably, three examples verified the effectiveness and superiority of the proposed framework in both linear and nonlinear relationships. As revealed from the results, the proposed interval model updating framework in the present study is suitable for coping with the updating problems of the parameter’s bounds and their correlations.



中文翻译:

基于相关传播和矩阵相似度方法的区间模型更新框架

模型更新技术已在实际系统中固有的不确定性的数值模型中获得了广泛的应用,而随机理论在知识不足的情况下是无效的。此外,面对相关的不确定性和复杂的数值模型,模型更新仍然具有挑战性。在本研究中,提出了一种新颖的区间模型更新框架来解决与极限样本相关的不确定性。这样的框架的优点在于,无论输入和输出之间的关系是线性的还是非线性的,都可以高精度地更新参数。为了实现此优势,分别采用凸建模技术和Chebyshev替代模型进行不确定性参数量化和数值模型逼近。随后,开发了考虑相关传播的矩阵相似度方法,建立了两步区间模型更新过程,并将其转化为确定性模型更新问题。所提到的过程简化了模型的复杂性,同时提高了更新结果的准确性。值得注意的是,三个示例验证了所提出框架在线性和非线性关系中的有效性和优越性。从结果可以看出,本研究提出的区间模型更新框架适合解决参数范围及其相关性的更新问题。所提到的过程简化了模型的复杂性,同时提高了更新结果的准确性。值得注意的是,三个示例验证了所提出框架在线性和非线性关系中的有效性和优越性。从结果可以看出,本研究提出的区间模型更新框架适合解决参数范围及其相关性的更新问题。所提到的过程简化了模型的复杂性,同时提高了更新结果的准确性。值得注意的是,三个示例验证了所提出框架在线性和非线性关系中的有效性和优越性。从结果可以看出,本研究提出的区间模型更新框架适合解决参数范围及其相关性的更新问题。

更新日期:2021-05-24
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