# PrimaVera: Synergising Predictive Maintenance
## 2 State of the Art
### Data Processing and Diagnostics  
Automated data validation and correction for predictive maintenance requires methods that work under realistic assumptions. Within statistics and machine learning, many different techniques have been developed for dealing with missing data [20; 21; 22]. Most existing techniques rely on the missing completely at random (MCAR) assumption, which does not apply to the typical sensor data relevant for predictive maintenance. Recent approaches based on Gaussian copulas [23; 24] can at least handle the missing at random (MAR) assumption, in which whether or not a data point is missing may depend on the values of other variables. A key challenge is to develop techniques that can further relax these assumptions and efficiently handle streaming big data, while at the same time identifying and correcting for outliers. Missing value imputation methods based on low-rank matrix completion such as [25; 26] provide a good starting point: they are computationally efficient and their implicit projection of high-dimensional data into a lower-dimensional space naturally facilitates the robust detection of outliers [27; 28].  
Monitoring is an essential part of condition based maintenance, since monitoring the condition of systems allows the early identification of imminent failures. Current monitoring methods are not yet suitable for automated use, since they fail when there is no labelled training data, cannot handle high-dimensional data streams, do not adapt to data arriving at different time scales or do not take into account internal dependencies [29] and are not capable of making use of physical models. Regression-based monitoring methods have recently been extended to obtain adaptive detection thresholds in high-dimensional settings [30]. A first attempt to develop self-starting regression-based monitoring methods that do not required labelled training data has been presented in [31]. Purely statistical approaches have the advantage of providing performance guarantees, but they are difficult to automate. A promising recent approach to overcome this, is to use deep learning to correct for internal dependencies and use statistical approaches for monitoring [32]. The PrimaVera project will build upon these approaches by developing automated approaches with guaranteed performance that work in realistic industrial settings. In addition to these data-driven condition monitoring techniques, also more physics-based structural health monitoring techniques will be developed. These techniques typically utilise the dynamic response of systems and structures (e.g., vibrations) to detect and assess the presence, location and severity of damage [33].  
To successfully design maintenance interventions, it is essential to understand why systems fail. The rapidly growing field of causal inference (see, e.g., the recent bestseller [34]) here may provide a solution. So-called transfer entropy [35] can be used to estimate the directed transfer of information between the time series of two variables, e.g., from sensors at different parts of a lithographic machine [36]. Causal discovery methods [37; 38] aim to unravel the causal structure underlying the interactions between many different variables from purely observational data. From a methodological point of view, a key challenge is to integrate these two approaches to go from pairwise measures of causal information flow to a graphical structure that can be efficiently queried to find the root causes of specific failures.  
Whereas causal inference has been successfully applied in various scientific domains (e.g., climate research [39], neuroscience [40], proteomics [41], psychology [42]), its application in industrial settings is largely unprecedented. A methodological challenge here is to estimate transfer entropy in industrial settings.