A rotary machine includes a rotatable member and a casing extending circumferentially over the rotatable member. The casing includes first and second target impingement surfaces. The cooling system includes first and second impingement plates. The first impingement plate is positioned over the first target impingement surface and at least a portion of the second target impingement surface. The first impingement plate defines a plurality of first impingement holes configured to channel a first flow of cooling fluid toward the first target impingement surface. The second impingement plate is positioned over the second target impingement surface. The second impingement plate defines a plurality of second impingement holes configured to channel a second flow of cooling fluid toward the second target impingement surface. A thickness of the casing in the first target impingement surface is different than a thickness of the casing in the second target impingement surface.