# A Novel Framework for Online Remaining Useful Life Prediction of an Industrial Slurry Pump
## 1 Introduction  
A smart Remaining Useful Life (_RUL_) prediction method is one of the most important elements of a Condition Based Maintenance (CBM) system. If a maintenance engineer has an idea for a running machine of when it will start to degrade, then he can take wise maintenance decisions beforehand. By doing so, he will not only save the industry from downtime but will also optimize the working of a particular machine by protecting it from unnecessary maintenance. There are three types of _RUL_ prediction methods that are currently available in the literature [1], model-based methods, data-driven methods, and hybrid approaches. If the physical model of the deterioration of a machine is precisely derived, then the model-based _RUL_ prediction approaches are suitable for _RUL_ prediction. However, accurate physical failure models are difficult to construct due to the increasing complexity of modern machines and components. With the rapid growth of the industrial internet of things (IIOT), a substantial amount of machine monitoring data is now available in modern industries. This data can be utilized for fault diagnosis and the prognosis analysis of industrial machines [2]. Hybrid approaches attempt to fix the constraints of individual data-driven and model-based methods by merging these techniques [3]. However, they still depend on the analytical model's availability [4]. As a result, data-driven approaches have become the most popular and preferred choice by the researchers for _RUL_ prediction purposes [5]. The prognosis of the _RUL_ of a running machine in its real-time is a difficult task. This job becomes more challenging when no historic failure data is available for a particular machine. In literature, many _RUL_ prediction studies are available where researchers have utilized their own empirical or publically available datasets, for instance, [6; 7; 8; 9; 10]. A very positive aspect of those datasets was the presence of a huge amount of run-to-failure (training data) and run-to-prior failure (testing data) data. Researchers utilizedthe available run-to-failure data for training of the models while run-to-prior failure data for testing of their developed models. There are two problems involved with the above-mentioned approach to _RUL_ prediction: (i) Experimental/simulation-based datasets or publically available datasets, e.g., NASA's CMAPSS dataset or PRONOSTIA dataset, etc., are developed in a controlled environment. In contrast, the field data is different and more problematic than the data obtained from an artificially organized environment. (ii) Even from the field, it is not possible to have a huge amount of run-to-failure data of many same types of equipment. The reason is that machines are never allowed to work until their failure in an industry. After a specified time period, machines are typically practiced with the Time Based Maintenance (TBM) to keep them well and in a good working condition. In the real world, it is almost impossible to have a huge amount of run-to-failure field data of a machine. However, it is still possible to have the run-to-prior failure data of a particular running machine to make an analysis for its _RUL_. In the conducted research, the run-to-prior failure vibration datasets of an industrial slurry pump were acquired while it was performing its operation. Slurry pumps are a special kind of centrifugal pumps that are typically used in the oil industry, especially for oil sand exploration. These pumps are typically installed in plants where they work under adverse conditions. Impellers of the slurry pumps have direct contact with the dense and rocky slurry mixtures, so they are subject to continuous wear [11]. Recently, some research has been conducted for estimating the Remaining Useful Lives of the slurry pumps. For instance, [PERSON] [12] constructed a method for predicting the _RUL_ of slurry pump impellers by integrating a sum of two exponential functions with relevance vector machines (RVMs).