Dynamic principal component analysis (DPCA) and its nonlinear extension, dynamic kernel principal component analysis (DKPCA), are widely used in the monitoring of dynamic multivariate processes. In traditional DPCA and DKPCA, extended vectors through concatenating current process data point and a certain number of previous process data points are utilized for feature extraction. The dynamic relations among different variables are fixed in the extended vectors, i.e. the adoption of the dynamic information is not adaptively learned from raw process data. Although DKPCA utilizes a kernel function to handle dynamic and (or) nonlinear information, the prefixed kernel function and the associated parameters cannot be most effective for characterizing the dynamic relations among different process variables. To address these problems, this paper proposes a novel nonlinear dynamic method, called dynamic neural orthogonal mapping (DNOM), which consists of data dynamic extension, a nonlinear feedforward neural network, and an orthogonal mapping matrix. Through backpropagation and Eigen decomposition (ED) technique, DNOM can be optimized to extract key low-dimensional features from original high-dimensional data. The advantages of DNOM are demonstrated by both theoretical analysis and extensive experimental results on the Tennessee Eastman (TE) benchmark process. The results on the TE benchmark process show the superiority of DNOM in terms of missed detection rate and false alarm rate. The source codes of DNOM can be found in https://github.com/htz-ecust/DNOM.

动态主成分分析（DPCA）及其非线性扩展，动态核主成分分析（DKPCA）被广泛用于动态多变量过程的监视。在传统的DPCA和DKPCA中，通过连接当前过程数据点和一定数量的先前过程数据点的扩展向量用于特征提取。在扩展向量中固定了不同变量之间的动态关系，即，动态信息的采用无法从原始过程数据中自适应地学习。尽管DKPCA利用核函数来处理动态和（或）非线性信息，但是前缀核函数和关联的参数对于表征不同过程变量之间的动态关系并不是最有效的。为了解决这些问题，本文提出了一种新的非线性动力学方法，称为动态神经正交映射（DNOM），它由数据动态扩展，非线性前馈神经网络和正交映射矩阵组成。通过反向传播和本征分解（ED）技术，可以优化DNOM以从原始高维数据中提取关键的低维特征。DNOM的优势通过田纳西州伊士曼（TE）基准测试过程的理论分析和广泛的实验结果得以证明。TE基准测试过程的结果显示了DNOM在漏检率和误报率方面的优势。DNOM的源代码可以在https://github.com/htz-ecust/DNOM中找到。非线性前馈神经网络和正交映射矩阵。通过反向传播和本征分解（ED）技术，可以优化DNOM以从原始高维数据中提取关键的低维特征。DNOM的优势通过田纳西州伊士曼（TE）基准测试过程的理论分析和广泛的实验结果得以证明。TE基准测试过程的结果显示了DNOM在漏检率和误报率方面的优势。DNOM的源代码可以在https://github.com/htz-ecust/DNOM中找到。非线性前馈神经网络和正交映射矩阵。通过反向传播和本征分解（ED）技术，可以优化DNOM以从原始高维数据中提取关键的低维特征。DNOM的优势通过田纳西州伊士曼（TE）基准测试过程的理论分析和广泛的实验结果得以证明。TE基准测试过程的结果显示了DNOM在漏检率和误报率方面的优势。DNOM的源代码可以在https://github.com/htz-ecust/DNOM中找到。DNOM的优势通过田纳西州伊士曼（TE）基准测试过程的理论分析和广泛的实验结果得以证明。TE基准测试过程的结果显示了DNOM在漏检率和误报率方面的优势。DNOM的源代码可以在https://github.com/htz-ecust/DNOM中找到。DNOM的优势通过田纳西州伊士曼（TE）基准测试过程的理论分析和广泛的实验结果得以证明。TE基准测试过程的结果显示了DNOM在漏检率和误报率方面的优势。DNOM的源代码可以在https://github.com/htz-ecust/DNOM中找到。