This is pretty well the background noise of the Internet. Since phpMyAdmin had such a poor security history it is not uncommon to see systems looking for instances of it running on the network. Chances are, that is exactly what is happening. There are a few things you could do to take action on such an activity, though which one, or ones, you choose will depend wildly on how your site is used.
Block It Entirely
Depending on who needs to access your web site, you could insert firewall rules to only allow access from specific addresses or address ranges. For example:
-A INPUT -s 198.51.100.50-m tcp -p tcp --dport 80 -j ACCEPT
-A INPUT -s 203.0.113.0/24 -m tcp -p tcp --dport 80 -j ACCEPT
This will specifically allow address from the host 198.51.100.50 and the network 203.0.113.0/24. Here the benefit is limiting your scope of access to a relatively small set, however you need to know every where access is required.
Rate Limit Connections
IPtables has built in support for rate-limiting. As an example take these firewall rules:
-A INPUT -i eth0 -p tcp --dport 80 -m state --state NEW -m recent --set --name WEB
-A INPUT -i eth0 -p tcp --dport 80 -m state --state NEW -m recent --update --seconds 60 --hitcount 8 --rttl --name WEB -j DROP
What this will do is limit each source address to only 8 connections within 60 seconds. These values may need tweaking, depending on your environment, but will certainly slow down any kind of brute force or fast scan.
Dynamic Detection and Blocking
There are a number of applications for doing this, but they all basically work the same way:
- Read specific log files for actionable events
- Compare events against some kind of scoring system
- Take action if meets criteria
One of the most popular (subjectivity alert) is probably an application called fail2ban. It will process a large variety of logs on your system, including SSH and Apache, and issue blocks for those source addresses that are committing "suspicious" behavior. Typically this would be adding a source IP drop rule in your host firewall. You mention that you are using Nginx as your web server, so you would have to research whether or not fail2ban, or what other product, would work for you.