The initramfs problem occur during the boot process in ubuntu. if you are facing this problem during start-up of system then follow the below steps :
Step 1 : Boot from the Ubuntu Live CD/USB
Step 2 : Open Terminal
Step 3 : type command 'sudo fdisk -l' in terminal. It will display the Hard disk drive size and other partition details.
Step 4 : Type 'sudo fsck -yv /dev/sdaX' and press enter (where 'X' is the '/' partition)
Step 5 : After this reboot the system and the problem would be solved.