# Method of Multilevel Adaptive Synthesis of Monitoring Object Knowledge Graphs
## 1 Introduction
When predicting the states of complex dynamic objects with numerous possible states, which depend on many external and internal factors, determining the possible transition rules by an expert's way may cause significant difficulties. Prediction errors may occur as a result of using static rules, as the rules may not take into account the peculiarities of object behavior that have not been reflected in the statistical data processed during their generation. Hence, it is necessary to define adaptive synthesis of monitoring object models, where the rules are applied at each step of the synthesis. To define the rules, we can use the context \(Context(t_{k})\), which is specified, based on the current state of the object and the data formed as a result of processing the values of its parameters collected by monitoring systems. Thus, the task of adaptive synthesis of the observed object models, which consist of providing of transition: \(G_{t_{k}}\overset{Context(t_{k})}{\rightarrow}G_{t_{k+1}}\), can be formulated as follows. It is necessary to determine the state of the monitoring object at the time point \(t_{k+1}\) under the condition of its operation at time \(t_{k}\) in context \(Context(t_{k})\). The state of the monitoring object at a certain point in time is determined by the state of its model elements--\(G_{t_{k}}=\left(V^{L}_{t_{k^{\prime}}}E^{H}_{t_{k^{\prime}}},\ E^{R}_{t_{k^{\prime}}},\ FV_{t_{k^{\prime}}},\ FE_{t_{k}}\right)\). The values for node and edge attributes \(V^{L}_{t_{k^{\prime}}},E^{H}_{t_{k}},\ E^{R}_{t_{k}}\) at each step are assigned from the sets of their admissible values--\(FV_{t_{k}},\ FE_{t_{k}}\) correspondingly. The range of admissible values of node and edge attributes depend on the values of the node and edge attributes from the previous synthesis step \(t_{k-1}\). \[FV_{t_{k}}(V^{L}_{t_{k-1}},E^{H}_{t_{k-1}},E^{R}_{t_{k-1}})\overset{Context(t_ {k})}{\rightarrow}FV_{t_{k+1}} \tag{1}\]  
\[FE_{t_{k}}(V^{L}_{t_{k-1}},E^{H}_{t_{k-1}},E^{R}_{t_{k-1}})\overset{Context(t_ {k})}{\rightarrow}FE_{t_{k+1}}. \tag{2}\]  
After defining the ranges of admissible values for node and edge attributes, it is possible to calculate the values of node and edge attributes of the model at the step \(t_{k+1}\)--\(V^{L}_{t_{k+1}},E^{H}_{t_{k+1}},\ E^{R}_{t_{k+1}}\):  
\[V^{L}_{t_{k}}(V^{L}_{t_{k-1}},FV_{t_{k}})\to V^{L}_{t_{k+1}} \tag{3}\]  
\[E^{H}_{t_{k}}(E^{H}_{t_{k-1}},FE_{t_{k}})\to E^{H}_{t_{k+1}} \tag{4}\]  
\[E^{R}_{t_{k}}(E^{R}_{t_{k-1}},FE_{t_{k}})\to E^{R}_{t_{k+1}}. \tag{5}\]  
Based on the considered transitions, the following functional dependencies between the elements can be determined:  
\[FV_{t_{k+1}}=\phi_{V}(FV_{t_{k}},V^{L}_{t_{k}},E^{H}_{t_{k}},\ E^{R}_{t_{k}}, \ Context(t_{k})) \tag{6}\]  
\[FE_{t_{k+1}}=\phi_{E}(FE_{t_{k}},V^{L}_{t_{k}},E^{H}_{t_{k}},E^{R}_{t_{k}}, \ Context(t_{k})) \tag{7}\]  
\[V^{L}_{t_{k+1}}=\psi_{V}(FV_{t_{k+1}},V^{L}_{t_{k}}) \tag{8}\]  
\[E^{H}_{t_{k+1}}=\psi_{E^{H}}(FE_{t_{k+1}},E^{H}_{t_{k}}) \tag{9}\]\[E^{R}_{t_{k+1}}=\psi_{E^{R}}(FE_{t_{k+1}},E^{R}_{t_{k}}) \tag{10}\]  
We propose a solution to the problem of adaptive deductive synthesis of monitoring objects, by defining the context at each step of the synthesis, based on the object parameter values coming from the monitoring systems, and applying policies that allow for a given context to determine the transition rules used in the synthesis.