This paper proposes a new knowledge management framework for spectrum selection under non-stationary conditions supporting a set of applications with heterogeneous requirements. In this respect, an optimization problem is formulated to maximize an aggregate utility function that captures the suitability of spectrum portions with respect to the various application requirements and a set of preferences for using the different spectrum bands. Motivated by the practical limitations when solving the considered problem directly, an alternative solution is proposed. It exploits a statistical characterization of the environment retained in the knowledge database of the proposed framework. To cope with the non-stationarity of the environment, a reliability tester is proposed to detect relevant changes in radio conditions, and update database statistics accordingly. Then, a knowledge manager exploiting these statistics is developed to monitor the time-varying suitability of spectrum resources. Based on this, a novel spectrum management is proposed to approximate the optimal solution of the considered problem. The results obtained in a realistic digital home reveal that, under stationary conditions, the proposed strategy performs very close to the optimal solution with much less requirements in terms of spectrum reconfiguration and measurement reporting. Furthermore, thanks to the reliability tester support, substantial robustness is shown when interference conditions become non-stationary, thus proving the practicality of the proposed solution. ; Peer Reviewed ; Postprint (published version)