Due to the extremely complex mechanism and strong non-linear characteristics of industrial processes, data-driven soft sensor technologies play a key role in the intelligent measurement of process industries. However, the information of the collected process data in the steady stage is quite limited and unreliable, causing the small sample problem. As a result, it becomes an intractable challenge to catch the nature of the process and build accurate soft sensor models. To solve this problem, this paper proposes a novel manifold learning based virtual sample generation method (Isomap-VSG) to generate feasible virtual samples in the information gaps for supplementing the original small sample space. To find data sparse regions reasonably, one kind of manifold learning methods called Isomap is used to visualize process data with high dimension. Then virtual samples can be generated by the interpolation method and extreme learning machine. The simulation results on a standard dataset and a real-world application demonstrate that, compared with other advanced methods, the proposed Isomap-VSG method can achieve better performance in terms of generating feasible virtual samples and improving the accuracy of soft sensor models using limited samples.

由于工业过程的机制极其复杂且非线性特性很强，因此数据驱动的软传感器技术在过程工业的智能测量中起着关键作用。但是，在稳态阶段收集的过程数据的信息是非常有限和不可靠的，从而引起了小样本问题。结果，要抓住过程的本质并建立准确的软传感器模型就成为一个棘手的挑战。为了解决这个问题，本文提出了一种基于流形学习的虚拟样本生成方法（Isomap-VSG），可以在信息缺口中生成可行的虚拟样本，以补充原始的小样本空间。为了合理地找到数据稀疏区域，一种称为Isomap的流形学习方法用于可视化高维过程数据。然后可以通过插值方法和极限学习机生成虚拟样本。在标准数据集和实际应用中的仿真结果表明，与其他高级方法相比，所提出的Isomap-VSG方法在生成可行的虚拟样本以及使用有限的样本提高软传感器模型的准确性方面可以实现更好的性能。 。