How can a commit in git submodule trigger a build in continuous integration？

Based on @VonC 's question, I solved this problem. Ref https://developer.github.com/webhooks/configuring/

1. I set up project Monitor, which has two submodules, project A and B
2. Create file trigger.rb in project Monitor

require 'sinatra'

post '/payload' do
  system("git submodule update --remote")
  system("git add .")
  system("git commit -m Record_new_change")
  system("git push")
  puts "Finished handling"
end

3. Download ngrok, run it on a VPS or a long running commpuer with ./ngrok http 4567. You may got a link like http://7e9ea9dc.ngrok.io
4. Run ruby trigger.rb
5. Fork project B to B', write another script to make sure that all the commits are synchronized to project B'
6. Go to project settings page, create a new webhook, whose url is http://7e9ea9dc.ngrok.io/payload for project A and B'
7. Add project Monitor to Travis CI

In this way, the development for A and B is untouched, and the new builds can be triggered automatically.

A commit in project B would not trigger a build in project A

That is expected, considering B has no idea A exists.

You would need to record the new state of B (new gitlink, special entry in the index) of project A by doing:

cd /path/to/projectA
git submodule update --remote
git add .
git commit -m "Record new B SHA1 gitlink"
git push

git submodule update --remote will update submodule B to the latest commit of the branch recorded in A .gitmodules file for B.
See "git submodule tracking latest" and "Git submodules: Specify a branch/tag"

Then a new Travis build would be triggered for A.

If you want to automate the sequence described above, you would need a webhook (GitHub) (or BitBucket) for projectB, and a local listener which, on a push event on repo B, would trigger the commands mentioned before in a local repo of project A.