You can't spend money after guessing at the problem. I think you have a faulty piece of equipment delivering spikes to the loudspeaker driver. Now this could be a defect in the unit to which it is connected, or the amp in the sub. Disconnect the sub from your receiver or what ever is powering it. Leave it on and see if the thumps still occur. If they do you sub is faulty and most likely has a bad cap. If the sub is silent, and the thumps return after reconnection, then it is the sending device.
My hunch is it is he sub as you think it still occurs with the main amps off. You really have given little information on your set up, as is usual. Trouble shooting at long range is very difficult, and without ALL the details likely to lead to some wrong conclusions. My strong sense is though, that your Velodyne sub needs service.