In the process industry, it is essential to establish a data-driven soft sensor to predict the key variable that is difficult to online measure directly. The accuracy performance of data-driven soft sensors relies heavily on data. Unfortunately, it is hard to acquire sufficient and informative data from the samples with limited number, which is called as the small sample problem. For handling the small sample problem, it is a good solution to generating virtual samples according to the distribution of original data. This paper proposes an enhanced method of virtual sample generation utilizing manifold features to develop soft sensors using small data. First, T-Distribution Stochastic Neighbor Embedding (t-SNE) is utilized to extract the features of input data. The main idea of generating virtual samples is to use the interpolation algorithm to obtain virtual t-SNE input features and then the random forest algorithm is utilized to get the virtual outputs using virtual t-SNE input features. Finally, virtual samples using the proposed t-SNE based virtual sample generation (t-SNE-VSG) can be achieved. For the sake of confirming the effectiveness and feasibility of the presented t-SNE-VSG, a standard data set is first used. What is more, a small data set from an actual industrial process of Purified Terephthalic Acid is used to establish a soft sensor model. The results from simulations show that the accuracy performance of the soft sensor established with small data can be effectively improved by adding the virtual samples generated by t-SNE-VSG. In addition, t-SNE-VSG achieves superior accuracy to state-of-the-art virtual sample generation methods.

在过程工业中，必须建立数据驱动的软传感器来预测难以直接在线测量的关键变量。数据驱动的软传感器的精度性能在很大程度上依赖于数据。不幸的是，很难从数量有限的样本中获取足够的信息，这被称为小样本问题。对于处理小样本问题，根据原始数据的分布生成虚拟样本是一个很好的解决方案。本文提出了一种增强的虚拟样本生成方法，利用多种特征来开发使用小数据的软传感器。首先，利用 T-Distribution Stochastic Neighbor Embedding (t-SNE) 来提取输入数据的特征。生成虚拟样本的主要思想是利用插值算法获得虚拟 t-SNE 输入特征，然后利用随机森林算法利用虚拟 t-SNE 输入特征获得虚拟输出。最后，可以实现使用所提出的基于 t-SNE 的虚拟样本生成 (t-SNE-VSG) 的虚拟样本。为了确认所提出的 t-SNE-VSG 的有效性和可行性，首先使用标准数据集。更重要的是，使用来自纯化对苯二甲酸实际工业过程的小数据集来建立软传感器模型。仿真结果表明，通过添加t-SNE-VSG生成的虚拟样本，可以有效提高小数据建立的软传感器的精度性能。此外，