System of Systems (SoS) is a new class of complex software systems resulting from the integration of several independent systems working together. Within a SoS, many participant systems may be integrated and deleted operationally over the time. Each system has an Architecture Model modeled at design time. Thus, the SoS' software architecture description is represented by an aggregated Architecture Model. This aggregated Architecture Model represents participant systems but not necessarily their interactions and communications over the time. In literature, several research studies addressed issues related to SoS. However, we noticed a lack of studies that address the problem of how to describe the whole SoS' software architecture for each change of a participant system over the time. Moreover, studies dealing with checking conformity between the whole SoS' software architecture description and the aggregated Architecture Model, are still lacking. This paper presents an approach for the discovery of SoS' software architecture description from execution traces. For this purpose, the proposed approach records execution traces of all participant systems belonging to the SoS, their interactions and communications in a data base. Then, our approach relies on mining techniques to extract software architecture from the data base and describes it via a model called Architecture Model. In addition, this paper offers a solution for checking conformity between the aggregated Architecture Model and the Discovered Model. The diagnosis results may suggest new rules/constraints to enhance the aggregated Architecture Model