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针对过程的非线性和动态特性,提出了一种基于核正交流形角不相似度的监测方法。利用两个流形子空间正交向量求取的内积矩阵的奇异值,构建基于核正交流形角的不相似度指标,量化评估标准集和测试集的流形子空间的统计量关系。首先,在多流形投影方法基础上,利用非线性函数将原始过程数据投影到特征空间;然后,引入Gram-Schmidt方法正交化投影向量,形成流形子空间的基向量;再次,对两个流形子空间的内积进行特征值分解获得核正交流形角,构建不相似度监测模型。该监测指标融合角度和距离度量,以更好地触发故障警报。最后,通过在田纳西-伊斯曼过程上的仿真实验验证了所提出算法的优越性.
Aiming at the nonlinear and dynamic characteristics of the process, a monitoring method based on the dissimilarity degree of nuclear orthogonal manifold was proposed. The singular values of the inner product matrices obtained from the orthogonal vectors of the two manifold subspaces are used to construct the statistical relationship between the dissimilarity index based on the nuclear orthogonal manifold angle and the manifold subspace of the test set. Firstly, based on the multi-manifold projection method, the original process data is projected into the feature space by using the nonlinear function. Then, the Gram-Schmidt method is used to orthogonalize the projection vector to form the basis vector of the manifold subspace. Thirdly, Eigenvalue decomposition of the inner product of manifold manifold space to obtain the nuclear orthogonal manifold angle and construct the dissimilarity monitoring model. The monitoring metrics incorporate angle and distance measures to better trigger failure alerts. Finally, the superiority of the proposed algorithm is verified by the simulation experiments on the Tennessee-Eastman process.