I believe noble is the first level where civs start attacking you if you fall behind in power. There are three ways to deal with this.
A) Build large army to stay ahead in power graph.
B) Start an early war and you will be ahead in the power graphs as long as you destroy a civ or two.
C) Play the diplo game carefully. Make friends with the more powerful civs. Every 5-10 turns go around looking at potential threats. Open the diplo screen, and mouse over a civ that is in red under the Declare War section. If the mouseover text says "We have our hands full" it means they are already engaged in a war, or they are about to enter one, and many a times they are about to declare war on you. If you feel that the civ is likely to attack you, and not another civ, go to a friendly agressive civ, and bribe them into war against the one you feel is going to attack. Don't go to war yourself though. Constantly bribe civs into war, so they are kept busy and never attack. I forget what article this is in, but there is a detailed one on this strategy in this forum.
Good Luck.