發展基於小波函數的PLS模型用於批次製程的品質監控

Developing Wavelet Functional PLS Models to Enhance Batch Process Monitoring

侯冠宇(Guan-Yu Hou)

指導教授 ： 陳榮輝

中原大學/工學院/化學工程研究所/碩士(2020年)

https://doi.org/10.6840/cycu202000435

摘要

在現代工業中，批次過程對於製造高質量產品相當重要，為了保證生產安全性以及提高產品質量，批次過程監控引起了相當多的關注。因此，如何有效地利用歷史的批次數據來建立快速且精確的過程監控模型是工業過程控制領域上的重要研究課題。在過去的過程監控方法中，即使批次過程的操作時間不同，批次之間的採樣點的長度也被假設為相同，因此對於批次不等長的數據將被對齊成批次等長數據後，再進行過程監控。由於以離散形式記錄量測到的變量，因此忽略了變量的連續特性。此外，大多數的監控方法都是在批次操作結束後才進行檢測。為了盡早檢測故障並發出預警，需要批內過程監控方法。
此研究提出一種新的小波函數偏最小平方模型，用於批次過程的故障檢測。在提出的方法中，對於每個過程變量可以通過小波函數來近似過程變量的軌跡。由於小波函數的平移和縮放特性，它非常適合處理批次過程局部區域的變化。由於過程變量由函數描述，因此無需擔心批次長度不同和系統的非線性行為且可以將PLS監視方法直接應用於函數空間以進行故障檢測。利用小波函數的局部特性，可以將過程變量的軌跡分為多個階段，並在每個階段進行監控，以實現批內檢測。數值例子和工業燒結過程實例證明了提出方法的有效性。
建立良好的批次過程監控模型非常有價值，但是產品品質數據難以得到，因此建立該模型的成本可能很高，這使得要獲取足夠建模的品質數據並不容易。因此，所提出方法的監視性能將受到建模數據數量的限制。為了提高模型性能，提出了一種基於高斯過程（GP）的模型遷移方法的概念，將其他可用源過程的信息轉移到目標過程中。利用提出的模型遷移方法可以達到快速訓練模型和增強模型可靠性的目的。開發該方法有兩個步驟，包括（1）由源過程構建的小波函數偏最小二乘模型，以及（2）基於高斯過程的遷移學習，透過GP從類似過程或工廠的可用數據中轉移知識，並藉由線性投影將源模型的預測轉換為目標過程的結果。通過數值例子驗證所提方法的特點，並顯示其對工業燒結數據的適用性。

關鍵字

批次過程 ； 偏最小平方法 ； 小波近似 ； 遷移學習 ； 過程監控

並列摘要

In the modern industry, batch processes are very important for the manufacturing of high-quality products. To ensure production safety and improve product quality, batch process monitoring has attracted considerable attention. Therefore, how to effectively use historical batch data to establish a fast and accurate process monitoring model is an important task in the field of industrial process control. In past process monitoring methods, the sample lengths among batches are assumed to be the same even though there are different durations among batch runs. The uneven-length batch data would be synchronized to obtain regular even-length data. As the measured variables are recorded in a discrete form, the continuous characteristics of the variables are neglected. Moreover, most current monitoring methods deal with end-of-batch detection. To detect faults and issue early warnings, within-batch process monitoring methods are needed.
This research proposes a novel wavelet functional partial least squares model for process fault detection in the batch process. In the proposed method, the trajectory of the process variable is approximated by the wavelet function for each process variable. Because of the shifting and scaling characteristics of the wavelet function, it is quite suitable for dealing with the change of the local area of the batch process. As the process variables are described by functions, there is no need to worry about the different batch lengths and the nonlinear behavior of the system; then the PLS monitoring method can be directly applied to the function space for fault detection. With the local behaviors of the wavelet function, the process models can be divided into multiple phases. The within-batch detection can be realized based on each sub-phase/range. A numerical case and a case of industrial sintering process are given to demonstrate the effectiveness of the proposed method.
A well-constructed batch model is invaluable, but it can be costly to construct the model because of the expense in acquiring the quality data. As a result, it is often difficult or even not possible to obtain enough quality data for modeling. Thus, the monitoring performance of the proposed method will be limited by the number of modeling data. To improve the performance, an idea of model migration approach is proposed based on the Gaussian process (GP) to transfer information of other available source batches into the target batches. The GP model is used to facilitate the migration of information and it focuses on the target batch process data. The proposed model migration approach can achieve the purpose of rapid model training and the enhancement of model reliability. There are two steps to develop the proposed method, including (1) wavelet functional partial least squares models constructed by the source batches, and (2) Gaussian process-based migration learning to transform the predictions of source models into the result of the target batch model through a linear mapping. GP can leverage the statistical approach to transfer the knowledge from available data of similar processes or plants. The features of the proposed method are presented via a math case study and its applicability to an industrial sintering data is also shown.

並列關鍵字

Batch process ； Partial least squares ； Wavelet approximation ； Transfer learning ； Process monitoring

參考文獻

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