How to find out /describe a controlled experiment we have carried out in order to evaluate if there is empirical evidence that UML class diagram structural complexity metrics are correlated with maintenance time?
The UML class diagram can be obtined by different methods. E.g. UML class diagramm can be obtined from programming language code by reverse engeenering. You must to specify your problem for concrete answer.
The question is a bit vague. One can safely assume that there is a relationship between the complexity of UML class diagram and maintenance effort. However, the relationship is not simple as you may have a relatively simple class diagram with complex algorithmic code. What specific type of maintenance are you looking for?