Refresh observableArray when items are not observables

Yes, you can call valueHasMutated function for your array:

yourArray.valueHasMutated();

EDIT:
If first didn’t help you can do ‘dirty’ refresh:

self.refresh = function(){
    var data = self.array().slice(0);
    self.array([]);
    self.array(data);
};

Here is working fiddle: http://jsfiddle.net/vyshniakov/FuEy6/2/