Aiming at the dynamic and nonlinear characteristics of batch process, a multiway dynamic nonlinear global neighborhood preserving embedding algorithm is proposed. For the nonlinear batch process monitoring, kernel mapping is widely used to eliminate nonlinearity by projecting the data into high-dimensional space, but the nonlinear relationships between batch process variables are limited by many physical constraints, and the infinite-order mapping is inefficient and redundant. Compared with the basic kernel mapping method which provides an infinite-order nonlinear mapping, the proposed method considers the dynamic and nonlinear characteristics with many physical constraints and preserves the global and local structures concurrently. First, the time-lagged window is used to remove the auto-correlation in time series of process variables. Second, a nonlinear method named constructive polynomial mapping is used to avoid unnecessary redundancy and reduce computational complexity. Third, the global neighborhood preserving embedding method is used to extract structures fully after the dynamic and nonlinear characteristics are processed. Finally, the effects of the proposed algorithm are demonstrated by a mathematical model and the penicillin fermentation process.

中文翻译：

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用于监控批处理的多路动态非线性全局邻域保持嵌入方法

针对批处理过程的动态和非线性特点，提出了一种多路动态非线性全局邻域保持嵌入算法。对于非线性批处理监控，核映射被广泛用于通过将数据投影到高维空间来消除非线性，但批处理变量之间的非线性关系受到许多物理约束的限制，无限阶映射效率低下且冗余. 与提供无限阶非线性映射的基本核映射方法相比，该方法考虑了具有许多物理约束的动态和非线性特性，并同时保留了全局和局部结构。首先，时滞窗口用于去除过程变量时间序列中的自相关。第二，一种称为构造多项式映射的非线性方法用于避免不必要的冗余并降低计算复杂度。第三，在处理动态和非线性特征后，使用全局邻域保持嵌入方法来充分提取结构。最后，通过数学模型和青霉素发酵过程证明了所提出算法的效果。