GTX Titan not identified in PCIe x4

Dear all,
I have an issue to get my GTX Titan identified by Ubuntu when it is at the PCIe x4, I`m sure my both GPUs are working, and the x4 slot is also working.
My environment is:
OS: Ubuntu 18.04 LTS
PSU: 1000W
GPU1: GTX 1080Ti
GPU2: GTX Titan

My board has 2 PCIe 16x and 4x, both GPUs work at PCIe 16x. But only the 1080Ti is identified by lshw at the PCIe 4x.
Of course I need to use the newer GPU at the 16x in order to maximize its performance. Since both works at the 16x and only the newer at 4x, my guess is there is something related to the Titan’s firmware.
I’ve already enabled 4G support at BIOS, and have tried to find the GTX Titan at x4 with lshw, lspci and hwinfo without success. Dmesg and Kern.log also don’t show any relevant info.
Would you have any recommendation?
Thanks in advance,