# A Novel Fault Diagnosis Method for TE Process Based on Optimal Extreme Learning Machine
## 1 Introduction  
The chemical industry's equipment has grown increasingly automated, complicated, scaled-up, and intelligent as business has progressed [1; 2; 3; 4]. Furthermore, the chemical industry's intermediate products are frequently toxic and corrosive, making it possible for seemingly little errors to have notable safety consequences, making safety management challenging but increasingly critical: no mistake should be overlooked [5; 6; 7; 8; 9; 10]. As a result, in recent years, several novel ways to minimize maintenance costs and enhance the utilization of the production process have been investigated, one of which is timely fault detection and diagnosis. There are three types of fault detection and diagnosis for chemical processes: quantitative, qualitative, and historical process data-based methods [11; 12; 13]. The third way only requires historical data and does not require a complicated and precise mathematical modeling of the process based on considerable a priori knowledge and time-consuming and difficult mathematical processes. It can be modelled by directly processing historical data [14]. The amount of data available to researchers has considerably expanded with the arrival of the information and big data era, making it challenging for quantitative and qualitative methodologies to meet the criteria for diagnostic accuracy and time. As a result, in the chemical industry, data-based fault diagnosis methods are frequently used. Data-based diagnostic methods can be roughly categorized into statistics-based methods and machine-learning-based methods [15]. Initially, this class of methods was mostly based on statistical learning methods, and a number of scholars have suggested a variety of related statistical-learning-based methods for fault diagnostics of chemical processes. Principal component analysis [16], partial least squares [17], independent component analysis [18], and Fisher's discriminant analysis are the most common statistical-based methodologies [19]. All these methods aim to protect chemical variables from highly non-linear correlations and complex processes by reducing the dimensionality of the data to describe the main features of the original data while reducing noise and improving the computational complexity of high-dimensional data, among other things. However, as the number of data dimensions grows, the complexity of these statistics-based methodologies exponentially increases, resulting in dimension disaster [20; 21]. Support vector machines (SVM) [22], artificial neural networks [23], and Bayesian networks are examples of machine-learning-based diagnostic approaches. SVM has been used to diagnose gearbox [24], rotating equipment [25], and high-pressure water supply heater issues in thermal power units [26], among other things. In addition, least square SVM is applied to reference evapotranspiration prediction [27] and assessment of water quality parameters [28]. For complex chemical process fault identification, [PERSON] and [PERSON] suggested an upgraded naive Bayes classifier [29]. However, an accurate classification of failure modes under complex chemical conditions is still not easy, especially when the test data come from different operating conditions and different domain distributions. Therefore, classifiers with a better generalization ability have been developed to cope with the degradation of diagnostic performance due to fluctuations in working conditions. Extreme learning machines (ELM) and their derivatives have been employed in a variety of pattern recognition applications in recent years [30; 31; 32], and have shown a comparable accuracy and generalization performance to back propagation neural network (BPNN) and SVM. ELM and kernel ELM (KELM) [33] were used to classify objects with a domain bias in a recent study [34]. Based on the deep features recovered by the dynamic convolution neural network (DCNN) model, they were used as the top classifiers. In all cross-domain recognition tasks, KELM beat ELM and SVM, according to comparative tests.