## 3 Criteria for Assessing the Interface Connectivity and the Reconfiguration of the Module
### Assessment of the Interface Connectivity  
The interface connectivity needs to meet criteria defined as a parent and child relationships in the matrices. One relationship is the parent and child relationship between the plug interface location matrix \(M\) and the socket interface location matrix \(A\). All of the nodes of the pre-connected structural components of the plug interface should be located within the acceptance scope of the related socket interface. The other relationship is the parent and child relationship between the plug interface connection section characterization matrix \(Q^{\prime}\) (calculated from the matrix \(Q\)) and the socket interface acceptable range matrix \(B\). All the feature points on the connection section of the pre-connected structural components of the plug interface should be located within the acceptance scope of the related socket interface. The two interfaces can be interconnected when both the digital expression models of the plug interface and the socket interface satisfy the parent and child relationship. Figure 4: (**a**) Digital expression model of the plug interface; matrix \(M\) represents the location of components and matrix \(Q\) represents the connection section of components; (**b**) Digital expression model of socket interface; matrix \(A\) represents the interface location and matrix \(B\) represents the acceptable range. The specific assessment criteria for the connection between module interfaces are described as follows [19]:  
1. The interface types of the two pre-connected modules are different. The interface type of the pre-connected module is determined according to the layout direction of the interface of the structural components. For good complementarity and compatibility, the interface type of the two pre-connected modules needs to be different. 2. The interface node network fully overlaps. Taking the parent node of the plug interface as a starting point, the pre-connected module's node network of the two interfaces need to fully overlap. The digital expression for the full overlap condition reflects the first parent and child relationship (i.e., the parent and child relationship between the location matrix \(M\) and the location matrix \(A\)). This means the location coordinates of the corresponding nodes of the pre-connected structural components of the plug interface are all within the acceptance scope of the socket interface, as shown in Figure 5a,b. It is assumed that the pre-connected structural component (\(i\)) for the plug interface connects with the longitudinal pre-connected structural component (\(k\)) for the socket interface. The criterion for assessing the connectivity between these two structural components is reflected within the parent and child relationship between matrices based on the digital expression of the interface, as shown in Figure 5b. 3. The connection sections of the pre-connected structural components are matched. Based on the full overlap of the module interfaces, another condition is to satisfy the matching requirements of the shape and size of the connection section. With the digital expression of the interface, the condition reflects the second aspect of the parent and child relationship (i.e., the parent and child relationship between the connection section characterization matrix \(Q^{\prime}\) of the plug interface and the acceptance range matrix B of the socket interface). This means that all the feature points on the connection section of the pre-connected structural components of the plug interface  
Figure 5: (**a**) The connection relationship between structural component numbered (\(i\)) and structural component numbered (\(k\)); (**b**) The parent and child relationship between matrix \(M_{i}\) and matrix \(A_{k}\). are within the acceptance scope of the pre-connected structural components of the socket interface, as shown in Figure 6a,b.