## 1 Introduction
Despite the system's high level of complexity, process monitoring and simple univariate fault detection methods proved critical to ensuring that the control system has access to consistent data [9]. Consequently, efficient process control is strongly relying on the capability of detecting sensor faults before the extension of their undesired effects [10]. Failures that are detected early on can help avert further induced undesired plant performance consequences and breakdowns. In general, process monitoring addresses four different tasks: (1) fault detection, which indicates that something is wrong in the process operation; (2) fault identification (or diagnosis), which establishes the cause of the issue; (3) fault estimation, which determines the magnitude of the defect; and (4) fault reconstruction, which calculates the fault-free process variable values aimed to perform the operation in the presence of faults [11]. Traditional fault detection and isolation methods use a mathematical model of the system to detect and isolate faults. In order to reveal discrepancies between the fault-affected and fault-free circumstances, these methods employ state estimation, parameter identification techniques, and parity relations [12; 13; 14]. However, developing precise mathematical models that characterize all physical and biochemical phenomena that occur in industrial processes is often challenging and time costly. When analytical models are not available, knowledge-based approaches such as expert systems might be considered as an alternative or supplement to analytical model-based approaches [15]. However, the development of these knowledge-based systems also necessitates a significant amount of time and work [16]. Online field-installed probes and offline laboratory analyses are used in traditional monitoring of the process variables. Real-time monitoring is difficult to be implemented, expensive and time-consuming. Field instruments require frequent and qualified maintenance, and the lack of satisfying these demands often makes the field measurements unreliable. On the other hand, time implied by laboratory measurements may range from a few minutes to several days to build a trustful assessment of the most standard wastewater monitoring metrics [17]. Both hardware and soft sensors can manifest a series of problems. While hardware sensors require a long time for maintenance and calibration, they exhibit insufficient accuracy and high noise levels. Their accuracy can quickly deteriorate in time and propose the support of soft sensors that can solve some of these issues. The soft sensors may also be subjected to faults as they rely on some sensor measurements and might depend on insufficiently accurate models [18]. As a result, detecting fault-affected measurements among the recorded data is critical for obtaining high WWTP effluent quality results. Sensor deficiencies and techniques utilized for detecting, amending and identifying faulty information or broken sensors were studied in a few works using different multivariate statistical process control (MSPC) methods, such as principal component analysis (PCA) [19; 20; 10; 21], independent component analysis (ICA) [22; 23], partial least squares (PLS) [24; 25; 26] or control charts [27; 28]. Dynamic multiblock partial least squares (DMBPLS) was implemented to detect chemical oxygen demand (COD) bias and pH drifting sensor faults at a Chinese papermaking wastewater treatment plant [29], while a combination of t-distribution stochastic neighbor embedding with a Gaussian mixture model (t-SNE-GMM) was proposed for detecting bias, drift and complete failure sensor faults in a similar plant [30]. Because of their natural identification limit, MSPC techniques show high potential and are proficient in observing the sensor deficiencies occurring in time-varying, poorly characterized and nonlinear behavior framework of measurements in wastewater treatment plants [31; 32; 33].