# Method of Multilevel Adaptive Synthesis of Monitoring Object Knowledge Graphs
## 4 Adaptive Synthesis Method Description  
The adaptive synthesis method is designed to transform the model of the monitoring object \(G_{t_{k}}\), describing an object at a point in time \(t_{k}\), into the object model at the moment of time \(t_{k+T}\)--\(G_{t_{k+T}}\). During the synthesis, the policies \(\overline{P}_{S}\) are defined, depending on the context as well as the related rules, according to which the synthesis of the object model is performed.  
The following are the input data for the adaptive multilevel deductive synthesis method:* The time interval at which the synthesis of the model of the monitoring object is performed [\(t_{k}\);\(t_{k}+T\)].
* Synthesis step--\(\Delta t\).
* Model of the monitored object, in which the values of the attributes at the moment \(t_{k}\)--\(G_{t_{k}}\).
* Policies used for model transformation \(\mathfrak{s}_{k,k+1}\):\(\overline{P}_{S}\).  
The output data for the method include the state of the monitoring object and values of its attributes at time \(t_{k+T}\)--\(G_{t_{k+T}}\).  
A formal description of the steps of the multilevel adaptive synthesis method are given below:  
1. Get the policies used for synthesis: \(\overline{P}_{S}:\overline{P}_{S_{1}},\ \overline{P}_{S_{2}},\ \ldots,\ \overline{P}_{S_{2}}\), where \(\overline{P}_{S_{i}}\)--the policy related to the context event \(S_{i}\), \(Z\)--the number of context events.
2. Obtain actual rules for synthesis of attribute values of model nodes and edges over time: \(P:P_{1}(G),\ P_{2}(G),\ \ldots,P_{N}(G)\), where \(N\)--the number of attributes.
3. Determine the current state of the object based on the data provided by the monitoring system at the time moment \(t_{k}\). Defining the node and edge attribute values of the monitoring object \(G_{t_{k}}\) taking into account the three-level gradation of their values: \(V_{t}^{att}=V_{i,1}^{atp},\ V_{i,2}^{attr},\ \ldots,\ V_{i,N}^{attr}\), where \(i\)--the node identifier, \(N\)--the number of nodes, \(E_{i}^{attr}=E_{j,1}^{atr},\ E_{j,2}^{attr},\ \ldots,\ E_{j,M}^{attr}\), where \(j\)--the edge identifier, \(M\)--the number of edges.
4. According to the data received from the monitoring system (step 3), or according to the synthesis results in the previous step (step 8), the definition of the context event \(S_{i}\subset S|G_{t_{k}}\).
5. Choose the policy \(\overline{P}_{S_{i}}\) based on the defined context event \(S_{i}\)--\(\overline{P}_{S_{i}}=p_{S_{i},1}\big{(}\overline{G}_{S_{i},t_{k}}\big{)}, \ p_{S_{i},2}\big{(}\overline{G}_{S_{i},t_{k}}\big{)},\ \ldots,\ p_{S_{i},N} \big{(}\overline{G}_{S_{i},t_{k}}\big{)}\), where \(\overline{P}_{S_{i}}\ S_{i}\)\(p_{S_{i},j}\big{(}\overline{G}_{S_{i},t_{k}}\big{)}\)--the rules, connected to the policy, \(W\)--the number of rules defined for the policy \(\overline{P}_{S_{i}}\), \(\overline{G}_{S_{i},t_{k}}\)--a subset of the attributes of nodes and edges, the state of which can change when a context event \(S_{i}\) occurs.
6. Using the selected rules, determine the set of acceptable values for nodes and edges at step \(t_{k+1}\): \[FV_{t_{k}+1}= \phi_{V}(FV_{t_{k}},V_{t_{k}^{\prime}}^{L},E_{t_{k}}^{H},\ E_{t_{k}}^{R },Context(t_{k}))\] (12) \[FE_{t_{k+1}}= \phi_{E}(FE_{t_{k}^{\prime}},V_{t_{k}^{\prime}}^{L},E_{t_{k}^{ \prime}}^{H},E_{t_{k}^{\prime}}^{R},Context(t_{k})),\] (13) as well as define values for parameters of nodes and edges: \[V_{t_{k+1}}^{L}=\psi_{V}(FV_{t_{k+1}},V_{t_{k}}^{L})\] (14) \[E_{t_{k+1}}^{H}=\psi_{E^{H}}(FE_{t_{k+1}},E_{t_{k}}^{H})\] (15) \[E_{t_{k+1}}^{R}=\psi_{E^{R}}(FE_{t_{k+1}},E_{t_{k}}^{R})\] (16)
1. The model of the monitoring object building at the step \(t_{k+1}\):\(G_{t_{k+1}}\) = (\(V_{t_{k+1}^{\prime}}^{L},E_{t_{k+1}^{\prime}}^{H},\ E_{t_{k+1}^{\prime}}^{R},\ FV_{t_{k+1}}^{R},\ FE_{t_{k+1}}\))
2. If \(t_{k}+1\ \geq t_{k}+T\), then \(G_{t_{k+1}}=G_{t_{k}+T}\)--the required model is built, otherwise, set the value \(t_{k}=t_{k}+1\) and go back to Step 4.