The E31 error in a Brother embroidery machine refers to a malfunction in the upper thread sensor. Here are some possible causes and solutions for the E31 error:

1. Check the thread path: Make sure the upper thread is properly threaded through the machine and that there are no obstructions or tangles in the thread path. Remove any tangled or damaged thread, and re-thread the machine following the instructions in the user manual.
2. Clean the machine: Check for any dust, lint, or debris that may be interfering with the thread sensor. Clean the machine thoroughly, especially around the bobbin area and the thread sensor.
3. Check the thread spool: The thread spool may not be seated correctly or may be too loose, causing it to wobble and affect the upper thread sensor. Make sure the spool is securely in place, and adjust the tension if necessary.
4. Check the upper thread sensor: The upper thread sensor may be malfunctioning or out of alignment. Contact a Brother service center or a qualified technician to repair or replace the sensor.

If the above steps do not resolve the issue, it is best to contact a Brother service center or a qualified technician for assistance.