## 2 Materials and Methods
### The Implemented Solution
The root node of the breadth-first traversals is always a weather feature, meaning that, starting from the weather features-predicted evolution, the algorithm can predict the evolution of the technical system tags, based on the identified dependency between the weather features and the system characteristics that were identified by the first-level algorithm. By executing the breadth-first traversal, all the existing relations between the technical system tags are considered in a global manner. For instance, if technical system characteristic A is directly influenced by temperature and technical system characteristic B is inversely influenced by A, the weather forecast indicating an increase in temperature for the following day, only computing characteristic A's new value based on the temperature increase, does not offer an accurate prediction of the system's overall evolution, because the increase in A causes a decrease in B as well. These kinds of cases are fully covered by the implemented algorithm, thus seeking to obtain a realistic prediction. The development of the _process_node_ function is based on:  
* computing the percent of change in the previous node (the node from which the arc leading to the current node starts), by comparing the previous node's current value and the node's previous day value. * computing the sign of change (if the previous node's value increased or decreased from the previous day). * using the percent of change in the previous node and the dependency from the graph, the predictive algorithm computes the percent of change for the current node (more details regarding the value of dependency in the graph can be found in [26]). * the percent of change for the current node is further used alongside the current value of the current node in order to identify the value of change (in units) for the current node. The value of change is onwards used together with the current value of the current node, the corresponding dependency from the graph, and the sign of change for the previous node, in order to compute the new value of the current node. The output of the implemented algorithm represents the predicted values for the monitored tags from the technical system for 7 d of the prediction. Thus far, the presented research implementation of the second layer follows a generic approach and can extend the water domain to any industry that relates to weather data. However, in order to apply and test the algorithm, a specific process is absolutely necessary. After implementing the second layer of the reference architecture, it became obvious that the relations and dependencies identification algorithm and the predictive algorithm could both receive a significant accuracy improvement by capitalizing on different process-specific information, which can be used during algorithm execution (e.g., knowing that a specific Open Platform Communications Unified Architecture (OPC UA) tag signifies the 'fault' code for a pump can be used during analysis in order to avoid false-positives identification for dependencies between the pump energy consumption and other values; knowing that from a process point of view, the aeration process requires a bluer that implicitly consumes energy; knowing process flow of the specific process; etc.). The process-aware Historian concept is essential for correct predictions, recipes, relevant data dependency analysis, and constraint and objective function interpretation. To be able to gather and use those process-specific information, the Historian application received a newly developed software module (Process Editor), which allows the creation of a model of a monitored process, inside the Historian application. Multiple processes can be defined, from which only one can be set as the currently used one, thus facilitating an easy switch between different monitored processes. Therefore, the process-aware Historian will request essential data mapping from the user according to the predefined process components characteristics.