Citation: Wang, Y.; Yang, D.; Peng, X.;
Zhong, W.; Cheng, H. Causal
Network Structure Learning Based
on Partial Least Squares and Causal
Inference of Nonoptimal Performance
in the Wastewater Treatment Process.
Processes 2022, 10, 909. https://
doi.org/10.3390/pr10050909
Academic Editor: Jie Zhang
Received: 14 March 2022
Accepted: 28 April 2022
Published: 5 May 2022
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Article
Causal Network Structure Learning Based on Partial Least
Squares and Causal Inference of Nonoptimal Performance
in the Wastewater Treatment Process
Yuhan Wang
†
, Dan Yang
†
, Xin Peng
†
, Weimin Zhong * and Hui Cheng *
Key Laboratory of Smart Manufacturing in Energy Chemical Process, East China University of Science and
Technology, Shanghai 200237, China; yh_wang@mail.ecust.edu.cn (Y.W.); dan.yang@mail.ecust.edu.cn (D.Y.);
xinpeng@ecust.edu.cn (X.P.)
* Correspondence: wmzhong@ecust.edu.cn (W.Z.); huihyva@ecust.edu.cn (H.C.)
† These authors contributed equally to this work.
Abstract:
Due to environmental fluctuations, the operating performance of complex industrial
processes may deteriorate and affect economic benefits. In order to obtain maximal economic benefits,
operating performance assessment is a novel focus. Therefore, this paper proposes a whole framework
from operating performance assessment to nonoptimal cause identification based on partial-least-
squares-based Granger causality analysis (PLS-GC) and Bayesian networks (BNs). The proposed
method has three main contributions. First, a multiblock operating performance assessment model
is established to correspondingly extract economic-related information and dynamic information.
Then, a Bayesian network structure is established by PLS-GC that excludes the strong coupling of
variables and simplifies the network structure. Lastly, nonoptimal root cause and and nonoptimal
transmission path are identified by Bayesian inference. The effectiveness of the proposed method
was verified on Benchmark Simulation Model 1.
Keywords:
nonoptimal cause identification; Granger causality analysis; Bayesian network; partial
least squares
1. Introduction
Along with the continuous development of industrial technology, the requirements of
modern industry are increasing. Process monitoring is no longer limited to fault detection,
and the operating state of industrial process with low economic benefits needs detection.
Even though nonoptimal operating state is not as serious as faults, it still affects the economic
benefits of the process. In order to ensure the economic benefits of processes, a nonoptimal
operating state needs to be immediately detected. Due to production environment changes,
equipment aging, parameter drift, etc., industrial processes may deviate from the optimal
state, showing multimode characteristics. Therefore, operating performance assessment is
increasingly important, and it divides operating conditions into an optimal and multiple
nonoptimal grades according to the economic benefits of the corresponding states. Due to
the high complexity of industry processes, it is difficult to establish a model according to the
process mechanism alone. Data-driven methods are attracting increasing attention [
1
,
2
], and
many basic data-driven methods were applied in performance assessment, such as principal
component analysis (PCA) [
3
]. Then, with the enlargement of data, complex characteristics in
these data have gradually attracted the attention of researchers. For example, in consideration
of the nonlinearity of the process, Liu et al. [
4
] put forward a method based on kernel
total projection to latent structures and kernel-optimality-related variations. Considering
the existence of process noise and outliers, Chu et al. [
5
] proposed a total robust kernel
projection to the latent structure algorithm. The above methods aimed at single-process
characteristic problems, while operating performance assessment was oriented to complex
Processes 2022, 10, 909. https://doi.org/10.3390/pr10050909 https://www.mdpi.com/journal/processes
