Hi,
Add this to your custom js:
function setYearFromDate(){
var date = spjs.utility.getDateFieldAsDateObject("YOUR_DATE_COLUMN");
setFieldValue("YOUR_YEAR_COLUMN",date.getFullYear());
}
Change YOUR_DATE_COLUMN and YOUR_YEAR_COLUMN to match your field names.
Add a rule in your form that triggers on change on the date column. Call the function setYearFromDate in the Run these functions / trigger these rules.
Let me know how this works out.
Alexander