Abstract It is of great importance to develop advanced soft sensors for ensuring the safety and stability of complex industrial processes. Unluckily, with the increasing scale of chemical processes, it becomes more and more demanding to develop soft sensor with high accuracy. In addition, most of industrial processes are dynamic. As a result, the soft sensors developed using static models cannot achieve acceptable performance. In order to handle this problem, the Echo state network (ESN) as a kind of recurrent neural network is selected. However, the output weights of ESN are calculated linearly. On one hand, the collinear in the reserve layer outputs may decrease the performance; on the other hand, the over-fitting problem may occur. To enhance and improve the ESN performance, singular value decomposition based ESN (SVD-ESN) is presented. In the SVD-ESN method, the singular value decomposition instead of the traditional least square is adopted to calculate the weights between the output layer and the reserve layer. Through singular value analysis in the outputs of the reserve layer, appropriate defining parameters are selected to enhance the accuracy and ensure the computing speed. As a result, the collinearity and over-fitting problem is solved; then the performance of ESN is enhanced. To test and validate the performance of SVD-ESN, the proposed SVD-ESN is developed as soft sensor for the High Density Polyethylene (HDPE) production process and Purified Terephthalic Acid (PTA) production process. Compared with the conventional ESN, Extreme Learning Machine (ELM), Dynamic Window based ELM (DW-ELM) and Long Short-Term Memory (LSTM), the simulation results show that the proposed SVD-ESN model obtains better performance in terms of prediction accuracy, which conforms that the proposed SVD-ESN can be used as an effective dynamic model for developing accurate soft sensors.

中文翻译：

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使用与奇异值分解相结合的回波状态网络开发新型软传感器：在复杂化学过程中的应用

摘要 开发先进的软传感器对于确保复杂工业过程的安全性和稳定性具有重要意义。不幸的是，随着化学过程规模的扩大，对开发高精度软传感器的要求越来越高。此外，大多数工业过程是动态的。因此，使用静态模型开发的软传感器无法达到可接受的性能。为了解决这个问题，选择了 Echo 状态网络 (ESN) 作为一种循环神经网络。然而，ESN 的输出权重是线性计算的。一方面，储备层输出中的共线可能会降低性能；另一方面，可能会出现过拟合问题。为了增强和改善 ESN 性能，提出了基于奇异值分解的 ESN (SVD-ESN)。在SVD-ESN方法中，采用奇异值分解代替传统的最小二乘法来计算输出层和储备层之间的权重。通过对后备层输出的奇异值分析，选择合适的定义参数，提高精度，保证计算速度。从而解决了共线性和过拟合问题；然后ESN的性能得到增强。为了测试和验证 SVD-ESN 的性能，建议的 SVD-ESN 被开发为用于高密度聚乙烯 (HDPE) 生产过程和纯化对苯二甲酸 (PTA) 生产过程的软传感器。与传统的 ESN、极限学习机 (ELM)、基于动态窗口的 ELM (DW-ELM) 和长短期记忆 (LSTM) 相比，