# A Novel Fault Diagnosis Method for TE Process Based on Optimal Extreme Learning Machine
## 1 Introduction
However, KELM still has some drawbacks, such as its being time-consuming and the laborious manual design of parameters, its heavy reliance on diagnostic experience, the limited ability of the shallow model to represent features, and its limited applicability under complex operating conditions. To further improve the diagnostic situation, we propose a new optimized KELM and apply it to solve the deterioration of the diagnostic performance due to complex conditions. Although research on machine learning methods in chemical process fault diagnosis has progressed, some problems remain to be solved. In chemical processes, some factors have negligible effects on the results, and too many variables consume computational resources. After obtaining process-monitoring data, the validity of the classification model must be determined. Long-term studies have shown that many features are not relevant to the classification goal. [PERSON] et al. classified data features into three categories: strongly correlated, weakly correlated, and irrelevant features [35]. Feature selection involves finding a subset of features that can be optimized and specified for evaluation criteria. Feature selection is also applied in many fault diagnosis methods. [PERSON] and [PERSON] proposed a PCA-based feature selection scheme [36]. [PERSON] et al. used Spearman's rank correlation coefficient to select variables from high-dimensional data to eliminate noise and redundant variables, thus reducing the dimensionality of chemical process data [37]. A Random Forest treebagger (RFtb) has recently been employed in the feature selection process for diagnosis in a variety of engineering fields [38; 39]. RFtb is one of the most accurate machine learning techniques, and performs well even when there are many input features and a limited number of samples [40; 41]. Additionally, RFtb has been to diagnose faults in gearboxes [42] and bearings [43]. Therefore, RFtb is also highly likely to achieve good feature extraction results in chemical process diagnosis. Inspired by previous works, we proposed a new fault diagnosis method for chemical process using Tennessee Eastman data. The method includes three successive procedures: feature extraction using RFtb, better optimization algorithms BCOA, and the fault detection method with BCOA-KELM based on the fused deep features. The methodological flow is as follows:  
1. Facing a time-varying, strongly coupled and nonlinear chemical dataset, we used RFtb to remove the redundant information while retaining most of the intrinsic and discriminative information to prevent features of different classes overlapping in some regions in the feature space. 2. We introduced chaotic mechanism and Bernoulli shift into COA, and proposed a new algorithm Bernoulli shift coyote optimization algorithm (BCOA). The algorithm is able to perform more accurate local exploitation in late iterations, speed up convergence, and better maintain the population diversity of coyotes in individual updates. We combined BCOA and KELM classifiers to improve KELM's being prone to fall into local extremes in the iteration. 3. BCOA-KELM was proposed and used as the top classifier for fault diagnosis based on fused multidomain features, taking advantage of both ensemble learning and multikernel learning. Our technique has better diagnostic abilities and a faster diagnostic speed due to its high generalization performance. The remainder of this paper is organized as follows. Section 2 presents the algorithm structure, the main components of the algorithm and the experimental methods. Section 3 compares the proposed method with other methods in terms of multidimensional indicators to demonstrate the superiority of this method. Section 4 provides a summary of this study and future work direction.