# Adaptive Imputation of Irregular Truncated Signals with Machine Learning
## 2 Literature Review  
CBM relies heavily on a data-driven approach, which makes the issue of missing data a significant challenge [1; 2]. Three of the most common reasons for missing sensor data include nonexistent attributes, temporarily unavailable data, and data loss or damage [4]. Missing data typically comes in three general types: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) [4; 5]. Potential cases where MCAR, MAR, and MNAR data can be found are air pressure systems [7], control charts [8], and sudden equipment failures, respectively. A more specific issue within this area is the problem of missing labeled data, particularly the loss of attributes, which poses significant challenges in real-world scenarios. In condition monitoring, the lack of labeled datasets from industry and the difficulty in transferring features from labeled lab datasets to unlabelled industry datasets are major obstacles [9; 10].  
One method for dealing with the problem of missing labeled data, particularly in datasets where there is un-labelled but annotated industry data, is to create joint representations of both textual annotations and sensor signals to allow a given model to learn from the relationships between the various data types [11]. Such a method was deployed in a study on condition monitoring in Swedish paper mills, where the authors found that this method could effectively bridge the gap between un-labelled data and intelligent fault diagnosis by utilizing the strengths of technical language processing and signal encoding [11]. While missing labeled data is a problem, our paper focuses on the problem of missing data in general. Traditional approaches for dealing with MCAR and MNAR data have included basic imputation methods such as listwise and pairwise deletion [5; 6], which can negatively influence decision-making processes [6].  
In Industry 4.0 environments, modern machine learning (ML) methods and multiple imputation methods have been employed to enhance data imputation models and improve decision making [5; 6]. In the case of MNAR data, Heckman correction and sensitivity analysis may be more appropriate [5]. Each of these methods has been applied to specific use cases in maintenance. Deletion methods were applied in [12] for the evaluation of historical system/component maintenance data, mean methods aided vibration analysis and CBM for a drying press in [13; 14; 15], regression methods were used for component replacement in railway flange lubrication and flexible degradation modelling and prognostics in aircraft engines, respectively, and hot deck methods improved learning and prediction in engineering data in [16]. Additionally, multiple imputation was used in [17] to predict the remaining useful life of a railcar, and in [18; 19; 20] ML methods were employed.  
The model we propose in this paper offers an improvement on the methods in the existing literature in several ways. First, many existing imputation methods do not adequately differentiate between MCAR, MAR, and MNAR data. Methods such as listwise deletion and mean imputation assume that data is MCAR, leading to biased and inefficient results when this assumption does not hold. Even more advanced methods like regression imputation may struggle with MNAR data, where the missingness is related to unobserved variables. Traditional imputation methods are often static and do not adapt to the specific characteristics of the dataset at hand. This can result in suboptimal imputations, particularly in datasets with complex missing data patterns. The limitations of existing methods highlight the need for a novel solution that can effectively handle various missing data mechanisms in an adaptive and computationally efficient manner. Our proposed framework addresses these challenges by integrating multiple ML-based imputation techniques within an adaptive system, providing a versatile and reliable solution for handling missing data in CBM systems.